its a druid quest chain to cure them iirc

Nope, that's the sickly deer or gazelle. There's no quests or explanations for the Corrupted creatures.

I always assumed it was because of the taint from Felwood that these animals were "sickly." But that may be because I play alliance and this is hinted at through the quests in Darkshore and in Felwood. But then again, I could be wrong, I had no idea that there were sickly animals in durotar, though there is a large demonic presence in the Barrens. That just makes the most sense to me.

It's implied they are corrupted b/c of the Burning Legion/Burning Blade cultists that are sulking around (Skull Rock - north Durotar and above the canyon north of Razor Hill, there is a cave there with the guys inside).

Its never explicitly said they are messing up the surroundings, but its implied by saying that they will destroy everything the Orcs have struggled to attain.

I had thoughts about the Felwood taint or the demonic influences as well, I suppose I'm just surprised that Blizzard never implemented anything to pull those into a quest of some sort. Seems like good potential to explain a bit of plot.

Checking wowhead comments suggests that these have greatly increased in proportion, relative to non-corrupted beasts, since patch 3.3. Same goes for "diseased" versions of animals in Elwynn Forest. Presumably there are similar changes in some other zones too. General theory seems to be some kind of pre-cursor to Cataclysm.

Well, you see when a mommy corrupted boar and a daddy corrupted boar love one another...

Easy, catch-all answer when they exist in a zone: Crazy Twilight's Hammer (or offshoots) Cultists did it.