I have recently been on a journey with this particular aspect of eschatology, and came to the conclusion, that based solely on scripture alone, our Father has not, and will never 'eternally punish' anyone.
I was also pretty surprised to discover (from reading the original language in OT and NT respectively) that 'Hell' is a word that was first introduced into scripture in the 12th Century by the Catholic Church in the Vulgate (Original 4th Century Latin translation) and is a concept firmly rooted in pagan beliefs.
Sheol and Hades on the other hand, are true places which are referred to in OT and NT in the original languages, and simply refer to 'a hidden place' or 'the place of the dead' or 'the grave or pit' - basically the grave.
When Jesus was speaking to the Pharisees, he made a statement about it being better to enter life maimed, then to be thrown into gehenna intact. He was referring the actual place Gehenna (or Valley of Himmon) which was the local rubbish dump, were bodies who were without paid tombs would be thrown - a place which continuously burned. A good visual metaphor for people to understand, but not the basis of a doctrine which includes god literally throwing the majority of the human population (almost 150 billion if you subscribe to a young earth) into an eternal flame to be tortured forever, without hope of ever being destroyed.
However, if you read most modern translations they have changed 'gehenna' (an actual place) into 'hell' (not an actual place).
Obviously there is a lot more to speak on, but that's a good start!
Find 'Hell' in the orignal scripture (not a translation) and I will give you my wife 
This is exactly why I often tell folks that I don't want them to be "eternally separated from God" because I don't know exactly what "hell" is or isn't.
I do grasp the eternality of God and the eternality of separation from him, but the "flames of hell". Literal? Figurative? Don't know.
I've heard defenses of both positions. I've read exactly what you noted. I've also searched out Sheol, Hades and Gehenna in lexicons and scoured articles for help. What I find is no consensus.
I think separation from God and all of his divine attributes is punishment enough. Will people experience the wrath of God's judgment? Absolutely. Will they have to come to terms with their choices and be separated from all of his goodness, mercy, grace, justice, love, etc.....? Yes.
We also read of "gnashing of teeth" and most associate that with the physical trauma, but people coping with mental stress and loss tend to gnash their teeth even more so.
Will folks simply be annihilated and cease to exist? Again I've read and heard both sides, but I don't think so. Still, existing in the flames of hell eternally doesn't seem reasonable, but I do believe God is just and that those that reject him will be dealt with accordingly. I've studied the "a temporary offense doesn't warrant an eternal punishment" objection and the apologetic response.....I discussed it on these boards.
What is the "fiery lake of burning sulfur"? Where is it? Depths of the earth? Another dimension? Literal? Figurative? The devil, false prophet and beast are indicated to burn in it forever. Will others be with them? What does that mean exactly? Is some of it literal and some of it figurative? Don't know....not versed enough.
Regardless, I choose to be aligned with Christ....that's who I want to spend eternity with. That's who I want others to come to know as well. The reality of the fates of the unbelievers I don't wish upon anyone because existing eternally or temporarily without God's divine attributes in that existence would be hell to me.
In this passage there is no mention of "hell", but the eternality of the after life is there:
Matthew 25:41-46
41 “Then He will also say to those on His left, ‘Depart from Me, accursed ones, into the eternal fire which has been prepared for the devil and his angels; 42 for I was hungry, and you gave Me nothing to eat; I was thirsty, and you gave Me nothing to drink; 43 I was a stranger, and you did not invite Me in; naked, and you did not clothe Me; sick, and in prison, and you did not visit Me.’ 44 Then they themselves also will answer, ‘Lord, when did we see You hungry, or thirsty, or a stranger, or naked, or sick, or in prison, and did not take care of You?’ 45 Then He will answer them, ‘Truly I say to you, to the extent that you did not do it to one of the least of these, you did not do it to Me.’ 46 These will go away into eternal punishment, but the righteous into eternal life.”What is the "eternal fire"? Literal? Figurative? What does the"eternal punishment" consist of? Something is going to happen and folks will be separated permanently from God and all he is. Are the "unquenchable fires of hell" the eternal realization of the implications of people's choices to be separated from God? Simply metaphors?
Yet the devil who knows his definite fate and will be cast into the lake of fire. No realization of separation from God will occur.....he's already separated and understands the ramifications. Seeks to manipulate God's creation into willfully rejecting God and joining him in that separation. So not a metaphor? Literal casting in burning sulfur?
Personally I have no desire to experience that situation. There's more to be said, but I've word vomited enough for this reply LOL.
