Jude is the only vs. which speaks of "eternal vengeance."
Paul used the word “aionios” eighteen [18] times. It is correctly translated “eternal/everlasting” 16 times and world only 2 times. In the following 12 verses Paul, Peter and John define/describe “aionios” as eternal.
Please pay particular attention to Rom 1:20, "aionios" and Rom 16:26, "aiodios" where Paul, the same writer, in the same writing, refers to God as “aionios.” Paul has used “aionios” synonymous with “aidios.” In this verse, by definition, “aionios” means eternal, everlasting etc.
[11]Romans 5:21
(21) That as sin hath reigned unto death, even so might grace reign through righteousness unto eternal [aionios] life by Jesus Christ our Lord.
In this verse Paul juxtaposes “aionios life” with death. “A finite age life” is not opposite death. “Aionios life” by definition means ‘eternal life.”
[12]Ephesians 3:21
(21) to him be glory in the church and in Christ Jesus throughout all generations, for ever [tou aionios] and ever! [ton aionion] Amen.
In this verse Paul parallels “tou aionios ton aionion” with “throughout all generations.” "Age(s)," a finite period, cannot refer to "all generations." By definition “tou aionios ton aionion” means forever and ever.
[13]Romans 1:20
(20) For the invisible things of him from the creation of the world are clearly seen, being understood by the things that are made, even his eternal [aidios] power and Godhead; so that they are without excuse:
[14]Romans 16:26
(26) But now is made manifest, and by the scriptures of the prophets, according to the commandment of the everlasting [aionios] God, made known to all nations for the obedience of faith:
In Rom 1:20, above, Paul refers to God’s power and Godhead as “aidios.” Scholars unanimously agree “aidios” unquestionably means eternal, everlasting, unending etc. In Rom 16:26, Paul, the same writer, in the same writing, refers to God as “aionios.” Paul has used “aionios” synonymous with “aidios.” In this verse, by definition, “aionios” means eternal, everlasting etc.
[15]2 Corinthians 4:17-18
(17) For our light affliction, which is but for a moment, worketh for us a far more exceeding and eternal [aionios] weight of glory;
(18) While we look not at the things which are seen, but at the things which are not seen: for the things which are seen are temporal;[proskairos] but the things which are not seen are eternal [aionios]
In this passage Paul juxtaposes “aionios” with “for a moment,” vs. 4, and “temporal,” vs. 5. “Age(s)” an indeterminate finite period, it is not the opposite of “for a moment”/”temporal/temporary” “eternal” is. “Aionios” by definition means “eternal.”
[16]2 Corinthians 5:1
(1) For we know that if our earthly house of this tabernacle were dissolved, we have a building of God, an house not made with hands, eternal [aionios] in the heavens.
In this verse Paul juxtaposes “aionios house” with “earthly house which is destroyed.” God is not going to replace our destroyed earthly house with a house which only lasts a little longer and will be destroyed at the end of an indeterminate age. The aionios house is not destroyed, the opposite of “is destroyed.” Thus, “aionios” by definition means “eternal.”
[17]1 Timothy 6:16
(16) Who only hath immortality, [aphthartos] dwelling in the light which no man can approach unto; whom no man hath seen, nor can see: to whom be honour and power everlasting [aionios]
In this verse Paul paralleled “aionios” with “immortality.” If “aionios” is only a finite age, God cannot be “immortal” and exist only for a finite age at the same time. Thus “aionios” by definition means “eternal.”
[18]Galatians 6:8
(8) For he that soweth to his flesh shall of the flesh reap corruption; [fthora] but he that soweth to the Spirit shall of the Spirit reap life everlasting. [aionios]
In this verse Paul juxtaposes “aionios” with “corruption.” “Fleshly” people reap “corruption” but spiritual people reap “life aionios,” i.e. “not corruption.” “Age(s), a finite period, is not opposite of “corruption.” Thus “aionios life” by definition means “eternal/everlasting life.”
[19]Romans 2:7
(7) To those who by persistence in doing good seek glory, honor and immortality, [apftharsia] he will give eternal [aionios] life.
In this verse Paul parallels “aionios life” with “immortality.” If “aionios” is only a finite period, believers do not seek for “a finite age,” and “immortality” at the same time. But they can seek for “eternal life” and “immortality” at the same time. Thus by definition “aionios life” means “eternal life.”
[20]1 Timothy 1:17.
(17) Now unto the King eternal, [aion] immortal, [aphthartos] invisible, the only wise God, be honour and glory for ever [aion] and ever [aionios]. Amen.
In this verse Paul parallels “aion” and “aionios” with “immortal.” “Aion”/”aionios” cannot mean “age(s),” a finite age and immortal at the same time. Thus “aion”/”aionios” by definition means “eternal.”
[21]Romans 5:21
(21) That as sin hath reigned unto death, even so might grace reign through righteousness unto eternal [aionios] life by Jesus Christ our Lord.
In this verse Paul juxtaposes “aionios life” with death. “A finite ‘age’ life” is not opposite death. “Aionios life” by definition means ‘eternal life.”
[22]Ephesians 3:21
(21) to him be glory in the church and in Christ Jesus throughout all generations, for ever [tou aionios] and ever! [ton aionion] Amen.
n this verse Paul parallels “tou aionios/ton aionion” with “throughout all generations.” "Age(s)" a finite period cannot refer to "all generations." By definition “tou aionios ton aionion” means forever and ever.
[23]Hebrews 7:24 but because Jesus lives forever [aion] he has an unchangeable [aparabatos] priesthood.
In this verse “aion” is parallel with “unchangeable.” If “aion” means “age(s),” Jesus cannot continue for only a “finite age” and simultaneously be “unchangeable.” Thus “aion” by definition means “eternal.”
[24]1 Peter 1:23
(23) For you have been born again, not of perishable seed, but of imperishable, [aphthartos] through the living and enduring word of God. …
1 Peter 1:25
(25) but the word of the Lord endures forever.[aion] " And this is the word that was preached to you.
In verse 23 Peter parallels “word of God” with “imperishable.” The same writer, Peter, in the same writing 1 Peter, in verse 25 writes the word of God “endures eis ton aiona/unto eternity. ” The word of God is not a finite age long but imperishable. Thus by definition “aion” means “eternity”
[25]1 Peter 5:10
(10) And the God of all grace, who called you to his eternal [aionion] glory in Christ, after you have suffered a little while, [oligon] will himself restore you and make you strong, firm and steadfast.
In this verse Peter contrasted “aionios” with “little while” Jesus does not give His followers a finite period of glory then they eventually die. Thus “aionios” , by definition, means “eternal.”
[26]Revelation 14:11
(11) And the smoke of their torment ascendeth up for ever and ever:[eis aionas aionon] and they have no rest day nor night, who worship the beast and his image, and whosoever receiveth the mark of his name.
In this verse “aionas aionon torment” is paralleled with “no rest day or night.” If “aionas, aionon” means “a finite age” at some time they would rest, “Aionas, aionon” by definition means “forever and forever.”
A final point about “aionios,” which is an adjective. “aionios” cannot be translated as “age” because age is a noun.