Witch covens as they appeared in Daggerfall and Bloodmoon were female spellcasters specializing in shapeshifting, the removal (and probably inflicting of) curses and daedra summoning. Unlike Skyrim, not all witches were hostile. The Corpse Preparation books mention Breton Witch-Kings, hough that's probably just shorthand for "generic wizard overlord". Oblivion also had a witch, who was responsible for aiding you in curing vampirism.
The Fryse Hags of Bloodmoon were basically evil Nord women spellcasters with an irritating fondness for frost magic.
The cliche cackling witch with her black cat and broom probably doesn't exist. 'Witch' is kind of a diverse term, but going by the Glenmoril Witches, those covens in Daggerfall and the Fryse Hags, you want a specialist of Restoration, Alchemy, Alteration, Destruction and Conjuration.
Remember that magic in the Elder Scrolls isn't cliche piercing voodoo dolls, chanting gobbledygook and gibbering at the moon. Magic is practically science; the Reman dynasties and the Aldmeri dominion had magically-fuelled spaceships while the Septim Empire had a space-station.
Lorewise, 'warlock' is actually an attainable rank of the Mages' Guild. The warlock class is...kind of weird and probably not applicable to the situation. Most posters seem to believe that warlocks are simply the WoW class, but anyway...
The distinctions are mostly arbitrary, but for clarification's sake...
Mages are pure spellcasters. They're the researchers who genuinely love their jobs both for practical reasons and because they really like their jobs.
Sorcerers tend to be egotistical mages who flatter their egos with daedric and undead servants, and are greedy for magical artifacts for the sake of power. They also seem to be paranoid, given that for the past few games they treated Heavy Armor as a class skill.
Battlemages are basically wizard-warriors decked out in heavy armor and trained in the use of heavy melee weaponry. Essentially, they hurl fireballs and conjure minions while bashing heads and cracking skulls.
Spellswords are magical mercenaries and skirmishers.
Nightblades are magical assassins.
Witch-hunters are a specific brand of mages dedicated to the purging of wicked daedra, evil mages, undead and so on. Basically, they're the arcane version of the Vigilants.
Necromancers are...well...lorewise the school of Necromancy draws on Conjuration, Restoration and Mysticism, but in-game you can just go around reanimating zombies and call yourself a necromancer.
Orcs...there doesn't really seem to be a cultural prejudice against magic among the Orsimer. Sure, there's that orc bookshop owner in Leyawiin who's irritated by his friends making fun of his reading habit, but the author of Corpse Preparation wrote that there were a few necromancers discussing petitioning King Gortwog on his views on Necromancy, and that Orc mage in Balmora is also a necromancer. They probably don't care so long as you're useful.