Here is a list of the Old Testament passages which Paul quotes from

Romans 3:10-12 from Psalm 14:1-3 and Psalm 53:1-3
Romans 3:13 from Psalm 5:9 and Psalm 140:3
Romans 3:14 from Psalm 10:7
Romans 3:15-17 from Isaiah 59:7-8 and see Isaiah 48:22
Romans 3:18 from Psalm 36:1

Psalms 10:7 His mouth is full of curses and deceit and oppression, under his tongue is mischief and wickedness.

Septuagint (LXX) of Ps 10:7 = οu aras to stoma autou gemei (3SPAI) kai pikrias kai dolou, hipo ten glossan autou kopos kai ponos. 

Mouth (4750) (stoma) refers to the bodily organ for eating and speaking.

Full of (1073) (gemo) means to be stuffed or filled full. To be full of something. The present tense pictures their being filled with cursing as a continuous process.

Cursing (685) (ara) (only here in the NT) originally it meant a wish, a petition, a prayer, but from the time of Homer it came to mean a prayer or invocation for harm or injury to come upon one, an imprecation (invocation of evil upon another), a curse which the deity was to execute. Eventually ara came to mean a malediction, the evil invoked, the mischief itself, the realized curse. In Greek mythology Ara was personified as the goddess of destruction and revenge. Cursing refers to wanting the worst for someone and publicly expressing that desire in caustic, derisive language. It represents open, public expression of emotional hostility against one’s enemy.

Full of cursing pictures constant cursing, as if ready to be spilled at the least provocation.

Preacher's Bible Commentary notes that...

The “curse” in New Testament times was not so much a “swear word” as we would think of it. It meant the use of words which of themselves held the power to bring about the desired effect of their malediction. Springing from a bitter root, this practice was prevalent enough to strike fear in the hearts of all, even to the point of death in some. (Briscoe, D. S., & Ogilvie, L. J. The Preacher's Commentary Series,  New Testament. 2003; Thomas Nelson)

Newell says

"To prove this, you need only take your stand upon any street, and strike upon the mouth a passerby. As well strike a hornets' nest! How men do curse others! Bitterness is ever ready! What fearful folly for a race speaking thus to imagine that by "being baptized, " and "joining the church" they are ready to "go to heaven, " and be in the holy company on high, with the meek and lowly Son of God and the holy angels, -and all this without a thought of being forgiven, washed, born again!" (Romans 3: Devotional and Expositional)

Spurgeon comments on Psalm 10:7 writing that

"Out of his own mouth he will be condemned. There is not only a little evil there, but his mouth is full of it. There is cursing which he spits against both God and men, deceit with which he entraps the unwary, and fraud by which, even in his common dealings, he robs his neighbors. Beware of such a man. Under his tongue. Deep in his throat are the unborn words which shall come forth as mischief and iniquity." (Treasury of David).

The Apostle James says that

“The tongue is set on fire of hell.”

Ray Stedman comments that...

"Cursing is blaming God; that is profanity. Bitterness is reproaching God because of the way he has run your life. This is what we hear all the time, even from Christians. We hear complaints about your circumstances, where God has placed you, and what he is doing with your life -- cursing and bitterness."   (Read the full text of the sermon Total Wipeout)

AND BITTERNESS: kai pikrias:

Bitterness (4088) (pikría from pikrós from pik- = to cut, prick) originally meant pointed or sharp, e.g., of arrows then more generally of what is “sharp” or “penetrating” to the senses, a bitter, pungent taste or smell and then what is “painful” to the feelings.

Pikria was used literally to describe plants that produced inedible or poisonous fruit.  Greeks defined this word as long-standing resentment, as the spirit which refuses to be reconciled. So many of us have a way of nursing our wrath to keep it warm, of brooding over the insults and the injuries which we have received.

In the NT pikria is used in a metaphorical sense to describe animosity, resentfulness, harshness or an openly-expressed emotional hostility against an enemy. Pikria defines a settled hostility that poisons the whole inner man. Somebody does something we do not like, so we harbor ill will against him. Bitterness leads to wrath, which is the explosion on the outside of the feelings on the inside.

Pikria is found 4 times in the NAS (Acts 8:23; Rom. 3:14; Eph. 4:31; Heb. 12:15)

Pikria is used 27 times in the Septuagint (LXX) (Exod 15:23; Deut 29:18; 32:32; Job 3:20; 7:11; 9:18; 10:1; 21:25; Ps 10:7; 14:3; Isa 28:21, 28; 37:29; Jer 2:21; 15:17; Lam 3:15, 19; Ezek 28:24; Amos 6:12)

In the first use of pikria in the OT Moses records...

And when they came to Marah, they could not drink the waters of Marah, for they were bitter (pikria); therefore it was named Marah. (Ex 15:23)

Bitterness reflects a smoldering resentment, a brooding grudge–filled attitude, an unwillingness to forgive or a harsh feeling. Bitterness is the opposite of sweetness and kindness (cf. husbands toward wives in Colossians 3:19 - see note). It harbors resentment and keeps score of wrongs (cf 1Cor 13:5)

Pikría or bitterness is  It is the spirit of irritability that keeps a person in perpetual animosity, making him sour and venomous. Bitterness applies to the bitterness of spirit to which men give vent by bitter words.

Barclay adds that

"the Greeks defined (pikría ) as long-standing resentment, as the spirit which refuses to be reconciled. So many of us have a way of nursing our wrath to keep it warm, of brooding over the insults and the injuries which we have received. Every Christian might well pray that God would teach him how to forget." (Barclay, W: The Daily Study Bible Series, Rev. ed. Philadelphia: The Westminster Press)

Eadie says that pikria is...

A figurative term denoting that fretted and irritable state of mind that keeps a man in perpetual animosity, that inclines him to harsh and uncharitable opinions of men and things, that makes him sour, crabby and repulsive in his general demeanor, that brings a scowl over his face & infuses venom into the words of his tongue.

Newell adds that their

"Bitterness is ever ready! What fearful folly for a race speaking thus to imagine that by "being baptized, " and "joining the church" they are ready to "go to heaven, " and be in the holy company on high, with the meek and lowly Son of God and the holy angels, -and all this without a thought of being forgiven, washed, born again!"  (Romans 3: Devotional and Expositional)

Wiersbe has this practical comment on "bitterness" to which even believers can fall prey (although here in Ro 3:14, the reference is of course referring to an unsaved individual):

"An unforgiving spirit is the devil’s playground and before long it becomes the Christian’s battleground. If somebody hurts us, either deliberately or unintentionally, and we do not forgive him, then we begin to develop bitterness within, which hardens the heart. We should be tenderhearted and kind, but instead we are hardhearted and bitter. Actually, we are not hurting the person who hurt us; we are only hurting ourselves. Bitterness in the heart makes us treat others the way Satan treats them, when we should treat others the way God has treated us. In His gracious kindness, God has forgiven us, and we should forgive others. We do not forgive for our sake (though we do get a blessing from it) or even for their sake, but for Jesus’ sake. Learning how to forgive and forget is one of the secrets of a happy Christian life." (Wiersbe, W: Bible Exposition Commentary. 1989. Victor)

In Acts Peter confronts Simon the sorcerer declaring

"I see that you (Simon) are in the gall of bitterness and in the bondage of iniquity" (Acts 8:23).

Comment: Note in Acts 8:13 "Simon himself believed" but his subsequent actions and Peter's assessment make it clear that this was not belief unto salvation but was intellectual and/or a belief only in the signs and wonders

Gall (chole gives us our medical term cholecystitis for gallbladder disease) is a bitter ingredient or bile and with pikría (bitterness), it conveys an extremely bitter, harsh, and distasteful condition, vividly picturing the reality of one in the bondage of iniquity. This verse then describes a spiritual poisoning—a heart of great wickedness—in Simon the sorcerer. The sin of bitterness, like all sin, is a harsh taskmaster, Solomon recording that a man's

"own iniquities will capture the wicked and he will be held with the cords of his sin." (Proverbs 5:22-notes) (Comment: Sin’s built-in consequences are inescapable)

Writing to the Ephesian saints Paul exhorted them to

Let all bitterness (pikria) and wrath and anger and clamor and slander be put away from you, along with all malice." (Eph 4:31)

In the final use of pikría in the NT, the writer of Hebrews exhorts his readers to

See to it (continually be on the lookout so) that no one comes short (to come too late, to be left out = if an unbeliever dies before trusting in Christ, he will be lost forever) of the grace of God; that no root of bitterness (in context this is the attitude of apostates within the church who are corruptive influences) springing up causes trouble, and by it many be defiled" (Heb 12:15-note)

MacArthur writes that in this context

"The root of bitterness refers to a person who is superficially identified with God’s people, and who falls back into paganism. But he is no ordinary apostate. He is arrogant and defiant concerning the things of God. He thumbs his nose at the Lord. God’s response to such boastful unbelief is harsh and final. “The Lord shall never be willing to forgive him, but rather the anger of the Lord and His jealousy will burn against that man, and every curse which is written in this book will rest on him, and the Lord will blot out his name from under heaven” (Dt 29:20)." (MacArthur, John: Hebrews. Moody Press )

David described cursing, bitter persons as those who

“have sharpened their tongue like a sword ... aimed bitter speech as their arrow, to shoot from concealment at the blameless; suddenly they shoot him, and do not fear” (Ps 64:3-4).

Every age of mankind, our own certainly included, has been characterized by people who use their tongues as vicious weapons. Their attacks not only are against those they know well enough to hate but sometimes, as David seems to intimate, even against strangers, simply for the perverse pleasure of venting their anger and hatred.

Torrey's Topic
Profane Swearing

THEIR FEET ARE SWIFT TO SHED BLOOD: oxeis oi podes auton ekcheai (AAN) haima: (Pr 1:16; 6:18)

In Romans 3:15-17 Paul is quoting from (Isa 59:7-8)

7 Their feet run to evil,
   And they hasten to shed innocent blood;
   Their thoughts are thoughts of iniquity;
   Devastation and destruction are in their highways.
8 They do not know the way of peace,
   And there is no justice in their tracks;
   They have made their paths crooked;
   Whoever treads on them does not know peace.

Whereas the preceding indictment was directed at men’s sinfulness as shown primarily by their words, in the next three verses Paul focuses his charges primarily against the conduct or actions of unredeemed men.

These three verses are almost like a condensed history of the world.

"For further details, read your daily papers!"

Every page of history attests the truth of this awful charge.

Their feet (4228)(pous = the part of the body used to stand and walk) Scripture frequently uses the path of one's feet as a  picture for one’s approach to life.

"The feet, as the emblem of walking, symbolize the whole conduct." (Godet)

Swift (3691) (oxús) had two basic meanings. Oxus refers to a keen edge for cutting, and thus meaning sharp, all of the NT uses with this meaning being in the book of the Revelation.

As used in the present verse, oxus pertains to that which is rapid in motion. Quick, meaning a very short period of time. Swift, nimble, probably since the idea of sharpness also implies eagerness. People apart from God are prone to violence. At the slightest provocation they commit murder.

Oxus is used once in Romans and 6 times in Rev 1:16-note; Re 2:12-note; Re 14:14-note; Re 14:17-note; Re 14:18- note

Oxus is used 11 times in the Septuagint (LXX) (Job 16:10; 41:30; Ps 14:3; 57:4; Pr 22:29; 27:4; Isa 5:28; 49:2; Ezek 5:1; Amos 2:15; Hab 1:8)

In secular Greek oxus had several nuances depending on the context -- Of feeling, sharp, keen, Of the sight, to be keenest of sight, to notice a thing sharply, to be quick of hearing. When referring to things that affect the sight oxus meant dazzling, bright, Of sound, sharp, shrill, piercing. Of  musical tones, sharp, high, Of taste, sharp, pungent, acid, Metaphorically of the mind, sharp, keen: quick to anger, hasty, passionate, sharp, quick, clever.

Shed (1632) (ekcheo from ek = out + chéo = pour) means literally to pour out causing something (in this case blood) to be emitted in quantity.

Blood (129) (haima) defines blood as the basis of life. Shedding of blood equates with committing murder.

Solomon writes that...

"If they say, “Come with us, let us lie in wait for blood, let us ambush the innocent without cause, let us swallow them alive like Sheol, even whole, as those who go down to the pit.. My son, do not walk in the way with them. Keep your feet from their path for their feet run to evil, and they hasten to shed blood." (Pr 1:11-12,15-16)

"Swift" denotes the readiness and eagerness of men to murder others, which in turn shows the dreadful malice and hatred that is in them.

Robert Haldane writes that

 “The most savage animals do not destroy so many of their own species to appease their hunger, as man destroys of his fellows; to satiate his ambition, his revenge, or [greed]." (An Exposition of Romans).

How swift are men to shed blood?

MacArthur writes that

"Even in the United States, with its Christian heritage, since the turn of the twentieth century twice as many of its citizens have been slain in private acts of murder than have been killed in all the wars of its entire history. According to researcher Arnold Barnett of the MIT, a child born today in any one of the fifty largest cities in the United States has the chance of one in fifty of being murdered. Dr. Barnett estimated that a baby born in the 1980s is more likely to be murdered than an American soldier in World War II was of being killed in combat." (MacArthur, J: Romans 1-8. Chicago: Moody Press)

Wayne Barber reminds us that

"the vengeance of lost man is incredible. We have seen it in many places, even in the heart of a little child when some other child takes his toy and he looks at him and says, "I hate you. I hate you. You took my toy. I wish you were dead." Where did that come from? Was he taught that in school? Was he taught that at home? No. It came from the fact that he was born depraved as a result of Adam’s sin. The vengeance of even a child shows us that man does not have any good in him whatsoever. If you ever think differently, you have missed the point of why the gospel is such good news." (Barber, Wayne. Notes on Romans)

Kent Hughes explains that...

"Man’s depravity is seen in his rush to violence. Will Durant wrote in his Lessons From History: "In the last 3,421 years of recorded history only 268 have seen no war." During World War II it was estimated that it took $225,000 to kill one enemy soldier. I wonder how much is being spent by the major nations today. Man loves violence!" (Hughes, R. K. Romans: Righteousness from heaven. Preaching the Word. Wheaton, Ill.: Crossway Books)

Ray Stedman wrote that...

"Someone has suggested that this would be a very remarkable verse to write above the doors of the United Nations building in New York: "Their feet are swift to shed blood, in their paths are ruin and misery, and the way of peace they do not know." Isn't it true? Here are the nations gathered together -- gathered to seek peace -- but the outcome of it is constant friction, and trouble, and disturbance, and heartache, and bloodshed, and misery, and they do not know the way of peace." (Read full text of sermon Peale or Paul?)

Torrey's Topic
Murder

DESTRUCTION AND MISERY ARE IN THEIR PATHS: suntrimma kai talaiporia en tais hodois auton:

The brevity of this statement belies its profundity. The truth is that man damages and destroys everything he touches, leaving a trail of pain and suffering in his wake! Mark it down. Wherever man goes, sin soon follows. Death and destruction follow his steps as night follows day.

Destruction (4938) (suntrimma from suntribo = break into pieces, crush completely) (only here in NT) literally describes that which is broken into pieces and shattered, resulting in total devastation. It was used to describe a fracture or broken limb (see LXX below).

Figuratively as used here in Romans 3 (the only NT use), suntrimma means destruction, decimation, calamity, ruin or that which is laid waste. A vivid word picture of what fallen man does to all he touches, whether it be "animal, vegetable or mineral"!

Suntrimma is used only once in the NT but 35 times in the Septuagint (LXX) most describing that which is broken, shattered or fractured. (Lev 21:19 = broken hand and foot; Lev 24:20 = fracture for fracture; Job 9:17; Ps 14:3; 60:2; 147:3; Pr 20:30; 23:29; Isa 15:5; 22:4; 28:12; 30:14, 26; 51:19; 59:7; 60:18; Jer 3:22; 6:14; 8:21; 10:19; 14:17; 17:18; 30:12; 48:3, 5; Lam 2:11; 3:48; 4:10; Amos 9:9)

Misery (5004) (talaiporia from talaiporos [Ro 7:24-note, Re 3:17-note] = afflicted, wretched, miserable, distressed condition in turn from tálas = suffering, wretched) is the general term that denotes the resulting harm that is always in the wake of man’s acts of destruction against his fellow man. His destructiveness inevitably leaves a trail of pain and despair. Talaiporia describes overwhelming hardship, trouble, suffering, calamity, misery or distress.

Talaiporia also describes the emotional condition that arises from inner or outer torment. In the present verse misery follows in the wake of man’s destructive acts against his fellow man.

Talaiporia is found 29 times in the Septuagint (LXX) (Job 30:3; Ps 12:5; 14:3; 32:4; 40:2; 69:20; 88:18; 140:10; Isa 47:11; 59:7; 60:18; Jer 4:20; 6:7, 26; 15:8; 20:8; 51:35, 56; Ezek 45:9; Hos 9:6; Joel 1:15; Amos 3:10; 5:9; Mic 2:4; Hab 1:3; 2:17)

The only other NT use of talaiporia is by James who writes...

Come now, you rich, weep and howl for your miseries which are coming upon you.  (James 5:1)

Path (3598)(hodos) when used literally describes any place along which one travels and moves from one place to another, and thus a way, a road, or a highway

Destruction and misery as Newell says is the

"epitome (embodiment or summary of) of human history. It is said that the ancient Troy of which Homer sang was built upon the ruins of an earlier Troy, -and that seven other Troys, each constructed upon the ruins of a former, have been found! ...Those who so loudly proclaim that the human race is "improving, "" progressing, " are blind deceivers, -blind to history, blind to present day facts, blind to the rising tide of human violence. "As it was in the days of Noah, " our Lord said, "so shall be the coming of the Son of Man." In those days of Noah the earth became "full of violence" (Ge 6:11)."  (Romans 3: Verse by Verse)

Denney says;

Wherever they go, you can trace them by the ruin and distress they leave behind.

Wayne Barber calls us to

Look back over human history and what do you have? You have the ruins of cities that have been destroyed by somebody else...Homer sang a song about the city of Troy, "The city of Troy is built on the ruins of an earlier city." Since the time Homer sang that song they have found seven more cities underneath the ruins. Now you say, "I haven’t killed anybody. I haven’t shot anybody. I am a pretty decent person." No...you have covered it over. It is like putting honey over the top of it, but underneath it is the same vengefulness. One of these days, the Lord Jesus is going to take the church out of this world and this world will for the first time see the hate that has been here, the depravity of man’s heart, wickedness like never before. Thank God we are not destined for His wrath. Thank God we have received the Lamb. (The full measure of man's destructiveness) is going to be seen one day. The only thing that is restraining it right now is the presence of the Holy Spirit in this world. (Barber, Wayne. Notes on Romans)

Mankind's tendency to destructiveness inevitably leaves a trail of deeply afflicted, dejected, and distressed men and women.

As Godet puts it man

oppresses (suntrimma) his brother, and fills his life with misery (talaipōría), so that the way marked out by such a course is watered with the tears of others...this overflow of depravity and suffering arises from a void: the absence of that feeling which should have filled the heart, the fear of God (v18). (Godet, F. Commentary on Romans).

Ray Stedman notes that...

Wherever man goes, ruin follows. Do we need any documentation of that today? Why do cities always develop ghettos and slums? Why do our beautiful mountains and streams become polluted? It is because of the heart of man. (Total Wipeout)
 

Robert Haldane comments that...

Men labor to destroy and to ruin one another; proceeding in their perverse ways, they cause destruction and misery. (Haldane, R. An Exposition of Romans).

Albert Barnes writes that...