Regarding aion and aionios a biased and errant understanding of these two words deals with so called eternal torment or punishment for most of mankind for a lifetime of sin with no salvation possible. First of all let's examine a scripture that shows just the opposite. Yes, there is a form of punishment for mankind as seen in 1 Corinthians 5:5, but from this scripture it does not include eternal torment. Instead it includes the opposite which is salvation.
1 Corinthians 5:5
5 hand this man over to Satan, so that the sinful nature may be destroyed and his spirit saved on the day of the Lord.
New International Version (NIV)
First of all in context this man's sins were large and even worse than what was preached or practiced by people in some of the pagan religions, a man having sexual relations with the wife of his father, as clearly written in 1 Corinthians 5:1.
1 Corinthians 5:1
1 It is actually reported that there is sexual immorality among you, and of a kind that does not occur even among pagans: A man has his father's wife.
Perhaps this was actually his mother by birth or his adopted mother. Which of these two is not stated here. However, clearly this is an example of man's sinful nature. When a person has such a sinful nature that cannot be corrected through truthful teaching to the individual the only other option for correction is for that person to reap what he has sewn or receive the harmful effects of his sin nature. In verse 5 this is through Satan, the God of man's sin nature with this man being handed over to Satan. The goal of God is the purification of man's sin nature or seeing this sin nature being destroyed as we see here and in other biblical verses. The goal is not punishment as this verse clearly states even this especially sinful man also will receive spiritual salvation on the day of the Lord or as the above verse states, "his spirit saved on the day of the Lord." Read in the same church epistle written by Paul 1 Corinthians chapter 15. This chapter tells us about natural bodies that all humanity has with its weakness and ultimate death and spiritual bodies raised in glory and power that we will receive thanks to Jesus Christ our Lord and Savior.
1 Corinthians 15:42-44
42 So will it be with the resurrection of the dead. The body that is sown is perishable, it is raised imperishable; 43 it is sown in dishonor, it is raised in glory; it is sown in weakness, it is raised in power; 44 it is sown a natural body, it is raised a spiritual body.
After this man in 1 Corinthians 5:5 experiences what Satan is here to do, which according to John 10:10 is steal, kill and destroy. Then perhaps when our loving God presents Himself to this man again he will finally accept it and not reject the truthful God, thereby avoiding more of the harmful and painful effects and nature of the deceiving and lying God of this world, Satan. This at least is God's goal so that at the end God will "be all in all". Otherwise what is the point of turning someone over to Satan? Does God or God's Son ever promote following Satan? No and Jesus Christ even cast out from people many demons which are spiritual beings under the authority of Satan. Jesus did this as part of the healing of people. See this in a number of verses, for example, Matthew 8:16, Matthew 9:33, Mark 1:34, Mark 1:39, and Luke 13:32. Jesus also taught and instructed his disciples so that they also cast out demons from people. See Matthew 10:8, Mark 6:13, and Mark 16:17. Here is the goal of Jesus Christ which is completed in verse 28 with, "so that God may be all in all".
1 Corinthians 15:20-28
20 But Christ has indeed been raised from the dead, the firstfruits of those who have fallen asleep. 21 For since death came through a man, the resurrection of the dead comes also through a man. 22 For as in Adam all die, so in Christ all will be made alive. 23 But each in his own turn: Christ, the firstfruits; then, when he comes, those who belong to him. 24 Then the end will come, when he hands over the kingdom to God the Father after he has destroyed all dominion, authority and power. 25 For he must reign until he has put all his enemies under his feet. 26 The last enemy to be destroyed is death. 27 For he "has put everything under his feet." Now when it says that "everything" has been put under him, it is clear that this does not include God himself, who put everything under Christ. 28 When he has done this, then the Son himself will be made subject to him who put everything under him, so that God may be all in all.
God has delegated all things pertaining to the church for the salvation of mankind under Jesus Christ his Son. We see in the above verses in Adam all die and in Christ all will be made alive. Since we have death for all of humanity, even Jesus Christ, we have in or through Christ all in the future made alive. This order of life after death is Christ first being raised from the dead. Then when He comes those who belong to him or the followers of Jesus Christ being raised from the dead. For an explanation of this see 1 Thessalonians 4:13-18. Next we see all dominion, authority and power destroyed with Jesus Christ reigning as King or ruler until He has put all, and this includes even his enemies, under his feet or rulership. Then the last enemy to be destroyed is death. In the original Greek, the word for destroyed (katargeoo) means "to render idle, unemployed, inoperative, to cause to cease, put an end to, do away with, annul, abolish". Death cannot be destroyed by there only being no further death. Death can only be destroyed and put to an end with the addition of a general resurrection. When death is finally destroyed this means no more death for humanity with all being made alive. When Jesus Christ finally reaches his goal of all or everything under His lordship or rulership, then Jesus Christ will turn back this authority to God his Father, so that God will or "may be all in all". This means all of humanity under God's commandments and with God's character, the foundation of which according to Jesus Christ as seen in Matthew 22:36-40 is to love God with all your heart and soul and love your neighbor as yourself.