Sheol is the Hebrew term used throughout the Tanakh, often it is translated "the grave," and is understood to refer to the final resting place of all the dead, both righteous and wicked. Gehenna is an Aramaic term that refers to the garbage dump outside Jerusalem (?), where worms gnawed on the refuse and where the heat of the decay would keep things constantly smoldering.
Tartaros and Hades both come from Greek, specifically from Greek myth. Hades is equivalent to Sheol, while Tartaros is used in the book of Jude, where the writer borrows the image from Greco-Roman myth of the Titans, bound in chains beneath the earth for resisting Zeus, to describe what God did to the angels who rebelled.
When the book of Revelation says that death and hell are thrown into the Lake of Fire, it means that death and Hades are thrown into Gehenna.
I'm aware of the Adventist doctrine of annihilation, that the damned simply cease to be after judgment, but I don't quite buy it. It doesn't square with my understanding of what Scripture presents, anyway.
But I find the notion of eternal hell, whether it's as picturesque as Dante and popular imagination makes it out to be, or not, odious. I don't like the concept of hell, and I especially hate how it's been depicted in popular culture, whether by cartoonists or by Pentecostal preachers pushing some twisted "Halloween alternative" like Hell Night.
It's one of those things about the faith that I find uncomfortable. There are many of them, and I suppose if I'm honest I'm looking for a reason not to believe them -- but I haven't found a valid one not to yet.