Destruction Warlock spells are themed after fire, explosions etc.
Elemental Shaman spells are themed after the 4 elements of WoW.
Frost/Fire/Arcane mages is a dead giveaway.
What exactly and where exactly are the priest spells based off of and where do they get their power from? More of a lore question I suppose, but its strange that we have a wide variety of spells that don't have much in common with eachother from a lore point of view.
We have "Vampiric" spells, so we sap the energy from people?
We have "Mind" spells, so we assault the target's thoughts and feelings?
We have a "Devouring Plague" spell... Wait, that sounds like a Death Knight ability.
We have "Void" spells, so we have knowledge of Old God magic?
Then we have our 2 Shadow Word spells which just implies shadow magic is a form just like Arcane.
What exactly does a "shadow priest" do?
Mind spells have to do with priests in general as priests heavily emphasize mental discipline and control (propaganda) this is probably a reflection of the real world where religion/priests are associated with both (in varying aspects, ie for mental discipline think of abstinence or eastern monks and vow of silences, etc).
Devouring Plague is legacy of racials, it was the undead priest racial when all priests had racial abilities. Fear Ward, Desperate Prayer and Hymn of Hope are also left overs from this era, with Fear Ward showing the fearlessness of dwarven priests and Hymn of Hope the inspiration of the Draenei. Removed however were Shadow Guard of the trolls, Starshards of the Nightelves (Tyrande still uses a similar ability, it's very close to Starfall). These abilities were deemed somewhat unbalanceable so they were either removed or given to all priests. (Chastize was also a racial and became Holy Word: Chastize.)
Void abilities do not correlate with Old Gods at all, but rather the absence of light. Think of Muru who was known as a Void Lord before being reborn into a being of light. The Void and Light are two ends of one axis so to speak. Void is emptiness or darkness.
Also, priests abilities use to have a few more "shadow word", for example Silence was called Shadow Word: Silence. And the opposite to these were "power word" such as Power Word: Fortitude and of course we still have Power Word: Shield, Power Word: Barrier and the new Power Word: Solace.
Power Words strengthen and protect, Shadow Words damage and weaken, Holy Words restore.
Lastly, I am not sure where you're getting these "elementals" themes from. There are other elements in WoW (for example there is a Sound Elemental), if you simply mean from resistances, Holy Resistance did exist at one point in time, it was just extremely rare and virtually never itemized. Because the theory goes Holy damage was divine and could not simply be resisted.
Shadow has a very Lovecraftian vibe to it, with the Void Tendrils, Psyfiend, Shadowfiend, the mind flaying and insanity themes etc. Similar to the old god / qiraj architecture, which are also heavily inspired by Lovecraft's Call of Cthulhu among others.
Many of the old god minions like the faceless ones use primarely shadow spells like Mind Blast, Mind Control, Mana Burn (removed priest spell) and Mind Flay, which suggests that Spriests tap into the same power as they do. Maybe even given by the old gods themselves.
Lovecraft is one of my biggest influences - I've always loved Shadow's ties to Lovecraftian themes
I was also kind of let down when The Dark Below turned out to not be the next WoW expansion - I was really hoping for a Lovecraft inspired expansion about Old Gods and Forgotten Ones, and lost sunken cities - and the incomprehensible malicious will of the Void