As far as I knew:
Phoenix was turned into a primal by the twelve (whom had been summoned by Louisoux in the attempt of sealing Bahamut) .
Odin's sword is the real primal (Odin is just a temptered victim that keeps praying so that the sword can be kept alive).
I didn't know about the difference between Primals and Eikons, but this might explains a few things.
Primals are the primary entity (the real "god"), then Eikons (anciente greek for image) are their representation / aberrations (what is summoned).
This wouldn't explain why Bahamut is regarded as an elder primal though.
Btw, where do they talk about paragons/reapers and eikons? I don't remember reading about them in the main quests ...