I know I have heard some of the names used for aeons from other places, but I can't place any of them. I have heard these names elsewhere but can't figure out where:

Shiva
Ifriti
Bahamut
Levithan

Are they maybe false gods worshipped by people in the past or something?

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First of all.. "Aeons" is only the FFX name.. Most people call them 'summons' :p

Shiva is a God in the Bhoedism (sp? o.O), If I"m right, and also a figure from a mitology. Also Ifrit is some ancient name..
I do't know about Leviathan, but most of these "Gods" or 'Deities' are from ancient history and mitology. They are by no means "false Gods" or something.
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Leviathan is a water snake/god in some ancient Mythe, Legend.
Bahamut has been known as King of the Dragons far longer then FF started to use 'm. :)
That's all i know :)

This site has all that info...

Final Heaven (http://finalheaven.org/guardians/squareart.shtml)

See the mythology on the side?

I'll give you Shiva as an example...

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Shiva [ hindu myth ]

Shiva in Hindu Mythology is actually a god(as in..male) and has nothing to do with ice o_O but I'll include it in here anyways. He was very uninterested in the matters of the world and materialistic things, such as jewels, gold or whatnot. He doesn't flow with the norm, hanging out with ghosts, gnomes, goblins, serpents..etc.

He prefers isolation and often sits atop Mount Kailas, meditating. Sometimes so intense that he becomes a pillar of fire. The gods wanted his wisdom and wanted him to marry so that they'd have warriors to protect the world. To accomplish this they asked for the help of goddess Shakti. She succeeded in becoming his consort and they had two sons. Ganesh and Karitkeya.

[ resource ]

Additional info:
The god Shiva had blue skin because he drank poison. Shiva is also a duality (life/death etc) that includes male/female.
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i heard something that leviathan is also the name of a creature from the bible thing or something like that

leviathan = Huge water breathing creature

apart from bahamut they're all name of various deities from various religeons

:alien:
all summons are named after some ancient god. odin is norse god of death. others are from other religions.

Shiva is a god in some current religion that represents death...or was it life and death.
Ifrit comes from myths about fiery spirits. They are also known as Efreet or even Jinn.
Leviathan is referred to in the Bible as being a giant creature that lives within the water, although I don't know much about him.
He is also used in various hebrew children stories along with Bohemoth and Ziz.

Er, yes, thanks for that, but just for future reference, please do not revive a thread that hasn't seen any posting activity for over six years (or generally even six months for that matter.) If it's been inactive for that long, then that generally means it's dead and nobody cares anymore. If you still really feel like you need to talk about it, though, you can start a new thread.