There are few myths that are mentioned explicitly (Hyne and Ultimecia seem to be two), but the creators have exported real mythological characters (Odin, Siren, Gilgamesh, Tiamat, Leviathan, etc...) into the game. It would seem to be reasonable that the myths about them came with them.

As for Ultimecia's knowledge of Diablos, the fact that she's from the future could explain how she knows about him. Any historical information that survives to her time could be used.

Mind you, this is all speculation. I'm not claiming this is true, it just could be.