The "gods" on Blazblue are all manmade creatures. (Takemakahara says on the CS Opening, to Rachel, that it is manmade. On ______ ________(have to look it up again) says Relius created Izanami. Amaterasu has a mechanical appearance, with what appears to be an led-type screen for a face.)
The 'gods' of BB include:
Takamagahara(char pg link) (img)
Amaterasu(glossry pg link) (img)
Izanami(char pg link) (img)
The Azure(glossry pg link) (img)
Most of them are an allusion to Shinto gods (ie as Izanami, Takemagahara, and Amaterasu). (Link to wiki pages on respective shinto gods) The Doomsday Izanami creates is alluding to the Christian philosophy of "rapture" (Link to wiki page on it). Her alternate title, Hades, is based on the god Hades(link to it) in Ancient Greek Mythology.
The Azure does not appear to be directly alluding to any real-world religious figure.