That's a really tough one. But, if I had to give my input, I'd say:
-Strongest: A tie between Hercules, Gilgamesh and Beowulf
-Weirdest: The stories involving Yokai. Any of them. They're really great.
-Most Interesting: I'd say Greek mythology, but that seems like a cop-out. In that case, I'd go for any mythology, other than Greek, because Greek is most heard-of, so any others would be new and interesting.
-Best Overall: I really love Greek mythology, but I've got to look more in-depth with the others, to make a more fair judgment. So far, the African and Asian and various European Fairy Tales have caught my interest, too.