Aiōnios = perpetual, eternal, everlasting.
Those who do not believe that the punishment of God in Hell is eternal literally change the meaning of the word aiōnios to mean age-long or for a set period of time. Such teachings as Universalism which teaches that all will eventually be saved (even Hitler) and Annihilationism which teaches that sinners after a short time of punishment will be destroyed and no longer exist hold to such a view.
In order to accommodate their distaste and rejection for the thought that a loving God could or will send sinners to Hell for eternity they have to tamper with this one word in order to minimise its meaning and to make it a short period of time.
In the above passages Christ uses the term aiōnios to define the length of the time of three distinct things:- fire, punishment and life. Please note that to change the length of the "punishment" of sinners and the length of time which the "fire" of their punishment will burn for would mean that one would have to change the length of the "life" which Christ mentions will be given to the "righteous." as soon as we tolerate false teachings they bring confusion to the simple meaning of the Scriptures. To tamper with one truth affects other truths. To minimise eternal punishment is to minimise eternal life. To make Hell a thing of time is to make Heaven a thing of time.
This word aiōnios is used 69 times in our New Testament. Seven of these times it is applied to Heaven (Lk.16:9); six times to the Gospel (Heb.5:9); three times to express the divinity of God (Rom.16:26); forty-four times in reference to the life that is given to the Christian (Jn.3:16); and lastly seven times in reference to the length of the punishment of the wicked (Mt.18:8; 25:41, 46; Jude 7; Mk.3:29; Heb.6:2; II Thess.1:9). So we see from this that to limit eternal punishment to a short period of time one must limit Heaven, the Gospel and God's divinity.
If aiōnios does not mean eternal or everlasting in these verses relating to the punishment of the wicked, as the Universalist and Annihilationist contend, then there is actually no other stronger word in the Greek language that could be used to mean an eternal age without end. Although this word when coupled with certain other Greek words may infer a period of time such as is revealed by its context like Romans 16:25 this is rare and not the normal meaning or usage of the Word in the NT.
Not only are we told by Christ that the punishment of the wicked is eternal but that the fire is eternal. It is called "everlasting fire." In Mk.9:43 Christ says of it: "the fire that never shall be quenched:" This statement is one word in the Greek: asbestos = not extinguished, perpetual, not to be quenched.
Also the smoke connected to the fire is depicted as eternal: "...he shall be tormented with fire and brimstone in the presence of the holy angels, and in the presence of the Lamb: And the smoke of their torment ascendeth up for ever and ever: and they have no rest day nor night..." (Rev.14:10-11). Added to the eternity of the punishment, the fire and the smoke, is the fact of them having "no rest day nor night." With all of these individual things connected to the future state of the lost there is never any inference of end.
The term "for ever and ever" is repeated 21 times in the New Testament and primarily in the Book of Revelation. Again because of how the word aiōn which is used here gets abused we must deal further with the word. It means age. When it is used concerning the present age it of course means a time period that has a beginning and end. When it used concerning the age to come in means an age unending without limit. Scripture talks of these two ages as distinct (Mt.12:32; Mk.10:30; Lk.18:30; Eph.1:21).
Every single time we read "forever and ever" (ages of ages) in the New Testament we read of an age without end. It never carries another meaninIn Revelation we read of the glory, blessing, honour and power due to Christ, His dominion, His life, of the reign of the saints with Him, and of torment of the beast and false prophet in the lake of fire as being "for ever and ever" (1:6; 4:9-10; 5:13-14; 7:12; 10:6; 11:15; 14:11; 15:7; 19:3; 20:10; 22:5).
There can be no doubt according to the written Scriptures that the final state of those who die without salvation in Christ is an eternal state of punishment, torment and fire.