In legend, Odin has only a single eye. He sacrificed one eye in exchange for knowledge/magic powers of some sort. A neat reference to this is in FFVIII, where you've got to remove eyes from statues and then replace them in order to access Odin. In FFVII, one of Odin's weapons is Gungir, but it's translated as "Gunge Lance" in the English script.

Ifrit (also spelled Efreet, Afreet, and other variants) is simply a spirit of a similar kind to the classic Genie, rather than a Balrog-like fire demon.

But then, none of the FF games are set in our world, so there's nothing to say the summon spells have to mirror their namesakes in our own mythologies. The fact that they're inspired by our legends is neat, but it'd probably be dull if they copied directly.

Hmm... aren't Bahamut and Behemoth simply different names for the same entity? I seem to recall that Behemoth is the name used in western and Christian texts, while Bahamut is in Islamic documents. Could be wrong about this, though.