The King of Dungeon Masters, Chris Perkins, gives a blast from the past, something from an ancient tome called Fiend Folio: here are described the four Elemental Princes of Evil that will be in the upcoming campaign adventure Princes of the Apocalypse.
Master Chris is giving suggest me another thought : Princes of the Apocalypse adventure narrates about 4 Elemental Evil Prophets that are linked with their Princes of Evil, here their connection:
If you want to dig in the knowledge about The Four Elemental Princes of Evil you need to search their alias: The Archomental.
In Planescape settings there’s the Planescape Monstrous Compendium Appendix III that well describes all of them and their relationship with the Tharizdun/The Dark God/Elder Elemental God, they are powerful but not demigod, they grant spell to their followers and yes, they can be slain.
If you want to play now a good prequel of Prince of the Apocalypse you can play Egg of the Phoenix adventure module where player characters must recover a powerful artifact and save an entire land from destruction by the Princes of the Elemental Evil.
Other references about four Princes are
There’s only an unanswered question: where’s the fifth prince? The real son of the Elder Elemental God, Cryonax, Prince of Evil Cold Creatures???