Possibly the strangest crossover I’ve seen, courtesy of TV Tropes, is The BSC, Vampire Slayers. It’s, well, a fusion of The Baby-Sitters Club and Buffy the Vampire Slayer.
The most random crossover I’ve found “in the wild” was Squirrel Talk, a Silmarillion/Emperor’s New Groove fic. Because both canons have characters that talk to animals, dontcha know?
The strangest I’ve seen so far is the Fallout/ My Little Pony crossovers.
What’s really weird is that you would expect to see a lot of first, second and third series MLP crossovers but they’re hardly any.
The Star Trek/ X-Men crossover was pretty weird. The new Star Trek/ Green Lantern crossover is strange as well. For weirdness you’d have a hard time beating the Looney Tunes/ Superman crossover.
The current Watchmen/ DC crossover is just plain stupid.
There was a wonderful Doctor Who and All Creatures Great and Small fanfiction crossover, for obvious reasons. But the kicker was that it also crossed over with Winston Churchill, the Wilderness Years (also for obvious reasons).
The weirdest one I saw was Teletubbies/Harry Potter. Don’t google it unless you want to read X-rated Snape-on-Teletubbies action.
Sure – the Doctor is roped into helping at a calving while Tristan is pressed into fighting off Cybermen. . . because no one can tell them apart. It writes itself, really.
Looney Dunes.
FanFiction.net used to have (it might still be up) a Band of Brothers/Futurama cross-over about the Planet Express crew accidentally crashing in the middle of Normandy during D-Day.
The fact that Band of Brothers is based on real people and actual events makes it even crazier as theoretically the people who were in the actual battle can read about themselves interacting with space aliens.