If you are going to consider the subject of the eternal torments of hell, you cannot limit yourself to the New Testament. You also should not limit yourself to English, but should also consider the usual words translated as "eternal" or the like in the Old Testament text.
Olam, Ad, and Nesah
One fairly common (439 uses) word in the Old Testament is the masculine noun, Olam (עוֹלָם), which is usually translated ever, everlasting, old, perpetual, or evermore. It is the word used to describe the effect of the tree of life in Genesis 3:22 ("live for ever"). It is also the word used to describe Jehovah as the "everlasting God" in Genesis 21:33 and the reign of God as being "for ever (עוֹלָם) and ever (עַד)" in Exodus 15:18. It's a word that typically refers to a long duration. So, even when it doesn't mean eternity, it means a long time (like the pre-flood "mighty men which were of old"). Sometimes olam is used in connection with an ordinance or law, such that it is designated a perpetual law. Many times we are told (especially in Psalm 136) that God's mercy endures for ever.
Ad (עַד) mentioned above in Exodus 15:18 is a less common word (49 uses) that has a similar sense of continuity. Sometimes it's used as a poetic variety word choice, as in Habakkuk 3:6, where it is parallel to olam, or Amos 1:11 where it is parallel to nesah (נֶצַח), or as an emphatic, as in Genesis 3:22 and Micah 4:5 where it is piled onto olam ("for ever and ever").
Nesah (נֶצַח) is used about as often (43 uses) as ad. While it is often translated as "ever," the connotation is more forward looking, as to a distant goal. In 1 Samuel 15:29 God is called the "Strength of Israel" using this word (נֵצַח יִשְׂרָאֵל) and this word translated as "Victory" is also treated as one of God's attributes, alongside greatness, power, and glory in 1 Chronicles 29:11.
Some Key Verses
There are a number of Old Testament verses that are key to any discussion about hell being a place of eternal torment.
Daniel's Two Resurrections
Daniel 12:2 And many of them that sleep in the dust of the earth shall awake, some to everlasting life (לְחַיֵּי עוֹלָם), and some to shame and everlasting contempt (לַחֲרָפוֹת לְדִרְאוֹן עוֹלָֽם).
In this verse, Daniel is given a prophesy about the general resurrection of both the righteous and the wicked. The former are resurrected to everlasting life, whereas the latter are resurrected to everlasting shame/contempt.
Isaiah's Contrasting Destinations
Isaiah 45:17 But Israel shall be saved in the LORD with an everlasting salvation (תְּשׁוּעַת עוֹלָמִים): ye shall not be ashamed nor confounded (לֹא־תֵבֹשׁוּ וְלֹא־תִכָּלְמוּ) world without end (עַד־עוֹלְמֵי עַֽד).
Of course, there are two ways of looking at this promise in Isaiah 45:17. One way is as a promise of endless (the use of "ad" twice and "olam" once is translated here as "world without end") protection from shame/confounding. This may indeed be the best way. The other way is as contrasting endless salvation with endless shame/confounding. Even if the former way is correct, when you compare Isaiah 45:17 with Daniel 12:2 it becomes clear that Daniel is making a claim about perpetual shame.
Imprecatory Psalm
Psalm 83:17 Let them be confounded and troubled for ever (עֲדֵי־עַד); yea, let them be put to shame, and perish:
In this psalm, Asaph prays for the wicked to be "confounded and troubled" "for ever" using an emphatic duplication of ad. Does Asaph have in mind the punishments of hell or merely the temporal punishments of this life? Perhaps it is the latter. Nevertheless, the perpetual administration of God's wrath on the wicked is the point being conveyed.
Unquenchable Fire
Isaiah 34:10 It shall not be quenched night nor day (לַיְלָה וְיוֹמָם); the smoke thereof shall go up for ever (לְעוֹלָם): from generation to generation (מִדּוֹר לָדוֹר) it shall lie waste; none shall pass through it for ever and ever (לְנֵצַח נְצָחִים).
"Day and night" is a Hebrew way of saying "constantly" or "without interruption." See, for example, Leviticus 8:35, Deuteronomy 28:66, Joshua 1:8, 1 Samuel 25:16, 1 Kings 8:59, 1 Chronicles 9:33, 2 Chronicles 6:20, Nehemiah 1:6 and 4:9, Psalms 1:2, 32:4, 42:3&8, 55:10, Isaiah 60:11, Jeremiah 9:1, 14:7, 16:13, 33:25(?), and Lamentations 2:18. It's the same reason that Jesus three day and night burial does not mean 6 half days, but instead an uninterrupted period that starts on the first day and ends on the third day.
The point about the fire not being quenched day or night is that there is no relief from the fire. It's not as though the fire burns for one hour and then there is a break. No, the fire is continual.
The endless (olam) ascent of the smoke is not that the column of smoke is a really high column that never gets to the top of the atmosphere. The endless ascent of the smoke is an indication that the fire continues forever.
The phrase "from generation to generation" (מִדּוֹר לָדוֹר)(midor lador) is another Hebrew idiom for "forever." See, for example, Exodus 17:16, Isaiah 13:20, 34: 17, and 51:8, Jeremiah 50:39, Lamentations 5:19, Daniel 4:3 and 4:34, and Joel 3:20. Mary uses this same idiom (as translated into Greek) in Luke 1:50. It's similar to the expression, "to all generations" (לְדֹר־וָדוֹר)(ledor vador) (Exodus 3:15 and numerous places in the Psalms). Likewise, Mary uses this idiom (as translated into Greek) in Luke 1:48.
To "lie waste" here refers to the land being, in essence, desert - ruined, destroyed, or the like.
Finally, the duplication of nesah (forever and ever) is used to describe the fact that one one will pass through the land. This seems to be connected to the idea that this a wasteland, as per the "lie waste." All the goodness of the land is gone.
Interestingly, though, this same verb, "to pass," is used like in English to refer to death. When someone dies, we say they passed away. I'm reluctant to dogmatically insist that the sense of this verse is that no one will die.
Fire that Burns Forever
Jeremiah 17:4 And thou, even thyself, shalt discontinue from thine heritage that I gave thee; and I will cause thee to serve thine enemies in the land which thou knowest not: for ye have kindled a fire in mine anger, which shall burn for ever (עַד־עוֹלָם).
This passage is not necessarily primarily about the fires of hell. Nevertheless, this verse demonstrates that the idea of God's judgment wrath burning like a never-ending fire is one Old Testament picture of God.
Everlasting Reproach, Shame, and Confusion
Jeremiah 20:11 But the LORD is with me as a mighty terrible one: therefore my persecutors shall stumble, and they shall not prevail: they shall be greatly ashamed; for they shall not prosper: their everlasting confusion shall never be forgotten.
Jeremiah 23:40 And I will bring an everlasting reproach upon you, and a perpetual shame, which shall not be forgotten.
I mention these verses as examples of God's never-ending judgment including not only pictures of physical suffering (like that caused by fire) but also of mental anguish (reproach, shame, and confusion). Hence the weeping/wailing and gnashing of teeth that Matthew mentions (link to post) or the darkness (fear) and furnace (pain) metaphors Matthew employs.
Psalm 9:5 Thou hast rebuked (גָּעַרְתָּ) the heathen, thou hast destroyed (אִבַּדְתָּ) the wicked, thou hast put out (מָחִיתָ) their name for ever and ever (לְעוֹלָם וָעֶֽד).
The heathen and wicked are the same group in mind, and rebuking them should be taken as something more akin to cursing them as opposed to just offering constructive criticism. Destroying them uses the word, abad, which we have seen above. The putting out their name here refers to something like blotting out or erasing their name. There is a similar expression in Deuteronomy 9:14, Deuteronomy 29:20, and 2 Kings 14:27. The 2 Kings reference refers to the LORD contrasting such a judgment with salvation. The Deuteronomy passages provide interesting parallels. Deuteronomy 9:14 says, "Let me alone, that I may destroy them (וְאַשְׁמִידֵם), and blot out (וְאֶמְחֶה) their name from under heaven: and I will make of thee a nation mightier and greater than they." Here the parallel word, a form of samad, is a very strong term for destruction. Similarly, Deuteronomy 29:20 states, "The LORD will not spare him, but then the anger of the LORD and his jealousy shall smoke against that man, and all the curses that are written in this book shall lie upon him, and the LORD shall blot out (וּמָחָה) his name from under heaven." Notice that here the cursing is explicit and God's negative disposition is described as "smoking."
While the putting out of their names could have various senses, it seems to have at least a negative psychological connotation, namely a reputational loss.
Psalm 78:66 And he smote his enemies in the hinder parts: he put them to a perpetual (עוֹלָם) reproach (חֶרְפַּת).
The hinder parts would be the rear ends of the enemies. Children get smitten there when they disobey their parents. Part of the punishment of God's enemies is the shame of being punished by God. The humiliation is part of the punishment.
Destroyed Forever / Perish Forever
Psalm 92:7 When the wicked spring as the grass, and when all the workers of iniquity do flourish; it is that they shall be destroyed (לְהִשָּֽׁמְדָם) for ever (עֲדֵי־עַֽד):
There are cases where the Old Testament uses "for ever" in the context of destruction, in a way that when taken in isolation may sound a bit like annihilation. Everlasting destruction can have a very different connotation from everlasting punishment. So, it's easy to understand how this verse could be interpreted as though the wicked will be permanently destroyed, if it were taken alone.
Job 4:20 They are destroyed (יֻכַּתּוּ) from morning to evening (מִבֹּקֶר לָעֶרֶב): they perish (יֹאבֵֽדוּ) for ever (לָנֶצַח) without any regarding it.
From morning to evening is another Hebrew way of saying "continuously" (Exodus 18:13, Exodus 27:21, and Acts 28:23). The first word translated "destroyed" (katat) here has the sense of receiving a beating or smashing. Thus, this is more of a picture of continually being struck.
The word for "perish" here (abad) implies death and seems to literally come from the sense of wandering away or being lost in that sense.
The best way of understanding this verse, however, is that the being destroyed and perishing are characteristics of humanity as such, and not about individuals. The point of the text is about how the human race is continually dying off.
Job 20:7 Yet he shall perish (יֹאבֵד) for ever (לָנֶצַח) like his own dung: they which have seen him shall say, Where is he?
The comparison here is interesting. Dung is (generally speaking) something which we make sure goes away, never to be seen by us again. The point is not just that the wicked will get temporarily misplaced but that he will be gone (abad) and not be coming back. By itself, this verse might seem to suggest that the wicked will not be resurrected. Nevertheless, we know from other Scripture that the death of the wicked is their end in this life only, but that they will face eternal judgment in the next life.
Numbers 24:20 And when he looked on Amalek, he took up his parable, and said, Amalek was the first of the nations; but his latter end shall be that he perish (אֹבֵֽד) for ever (עֲדֵי).
Numbers 24:24 And ships shall come from the coast of Chittim, and shall afflict Asshur, and shall afflict Eber, and he also shall perish (אֹבֵֽד) for ever (עֲדֵי).
Once again, the word for "perish" here is abad. The thing being discussed is the personification of Amalek. In the case of Amalek (as a nation), one can say that it was annihilated. You may recall that a significant destruction of the Amalekites came under Saul (whose failure to completely destroy them cost his family the kingdom) and then a further destruction of the Amalekites came under David (who killed all but 400 of them) and then the final destruction of the Amalekites came under Hezekiah. The verses don't have much to do with our subject, but I've included them anyway just for the sake of completeness.
Poetic Uses
Psalm 143:3 For the enemy hath persecuted my soul; he hath smitten my life down to the ground; he hath made me to dwell in darkness, as those that have been long (עוֹלָֽם) dead.
To dwell in darkness is here demonstrated to refer to those who have been dead for a while, as distinct from those recently deceased. It provides contrast to the beauty of Isaiah 9:2, "The people that walked in darkness have seen a great light: they that dwell in the land of the shadow of death, upon them hath the light shined."
Jonah 2:6 I went down to the bottoms of the mountains; the earth with her bars was about me for ever (לְעוֹלָם): yet hast thou brought up my life from corruption, O LORD my God.
I find this fascinating. Obviously, Jonah does not mean he literally was underground nor that he was literally there forever. Moreover, we know from the New Testament that the sign of Jonah was a sign of Jesus Christ. So, it is interesting to reflect on the sense in which Jonah's death forever under the earth, kept in by the bars of the earth (Hell's gates), was something that Christ experienced for us.
