Thanks for all the advice - here's an update -
After sorting through the rest of the donation I've now got probably got about 500 gallons of this nasty paint. Each bucket looks different and has varying levels of smell. Some have grey or reddish discoloration, and some resemble water more than others.
I've added a little bleach and used the paint, and I end up with a not quite rotted but still gross smell. The paint seems to be adhering fine (I sprayed exterior aluminum siding) and, probably because it is exterior, I can't notice a smell.
Interestingly, when I added the bleach the paint turned purple directly under where I had poured it in. After mixing it had a uniform white color. The paint is flat and does have a yellowish look to it, though I added color to the whites that I used in the field.
I'm still not really sure if bleach is a good idea or not. Some paint is fairly watery, and different buckets have different discoloration away from white. What I'm most afraid of at this point is that the binders and resins have degraded to a point that its not worth saving, though I have no idea how to tell which buckets are the worst.
That being said....it seems to stick fine and the smell, on the exterior at least, has gone away.
Thanks for the advice!