Is the explanation and backstory for the Alien creatures and the Predator creatures given in Alien v. Predator consistent with the information given in the indivdual Alien and Predator films?
No answer as I haven’t seen AvP, but this scathing review seems to indicate you shouldn’t take the AvP backstory too seriously.
The movie, or the countless video games, comics, and other media which preceeded it?
Given the insultingly stupid nature of the film. It doesn’t deserve any examination.
A movie that should be nuked from orbit.
The Predators are wildly inconsistent with their earlier movies (plus human history in general), the Aliens slightly less so, but keep in mind the latter’s films are set centuries in the future.
I don’t follow the Aliens and Predator comics, books, etc, so I don’t know if it’s all consistent. I think I’d be amazed if all the preceding stuff (including Batman vs. Predator and all such crossovers) were consistent with anything.
What I found interesting, when I finally caught AVP on cable, was that they finally found a way to use all that Alien hieroglyphic imagery they’d been tossing around since way back in the preproduction of the original film Alien, even before Giger came on board, but eventually had to jettison.
I haven’t seen the AvP movie, but the comic series which spawned the whole AvP franchise dedicated an issue or two to this subject. I don’t know if it was consistent at all with the numerous novels and whatnot, but it seemed to me pretty consistent with the movies at the time.
Seriously one of my favorite comics. I’m deeply sad they didn’t adapt this, I was looking forward to seeing the space-barge landing sequence at the end. 
Versus? I prefer Alien Loves Predator, myself.
(Yes, it’s work-safe. The “loves” is merely figurative…)