Let the theorizing begin!
(I would've put this in the Elantris section, but Peter did say "Cosmere")
Aside from thinking "Oh man! I'm totally adding all of this info into my wiki entries!" here are thoughts that occurred to me as I read:
1) All 3 are involved in the linking of Aon chains: Ehe to trigger, Ene/Omi to link
Significance: no idea
2) The discovery myth of Ehe
Significance: possibly drawn by a well-known, beloved, meddling planet hopper? Crazy theory, I know
3) Symmetry is discussed quite a bit
Significance: possibly none
4) It took "several decades" (which I'm interpreting as 2 generations) for the Shaod to affect the new inhabitants of Arelon. I think this tells us a little bit about how Shards interact with a people's Physical/Cognitive/Spiritual DNA
Significance: tons (depending on the question and once we get a little more info)
5) Omi "is one of the few Aons which requires something other than drawing skill from its Elantrian." Well, we love our exceptions.
Question: what are the other Aons like that?
[OK, most of those don't seem Cosmeric, but more Sel-specific]
6) Before Korath started referred to god with "Omi," the Elantrians used "Daa," which is the Aon for power.
Significance: it ties in with one of my yet-unpublished parts of the Unifying Theory of Magic. patience
7) "None are as strong without modification as Aon Ehe." Fire is somehow key/fundamental. Also, the effect of all 3 Aons is very light-heavy.
Significance: combine with the whole "Elantrians burn easily, mysterious fast-burning rocks from the south" it yields "der". also, it leads to the next one.
8) The description for Ehe really focuses it on how "primal" it is, how it's one of the primal elements.
Significance: That got me thinking:
Earth = metals
Fire = see #7
Air = breath
Granted, this is just the seed of a theory, and it doesn't include all magic systems. But there might be something there.
9) And, of course, the effects of the 3 Aons each fall neatly into a Realm:
Physical = Ehe (fire)
Mental = Ene (wit/cleverness/intelligence)
Spiritual = Omi (love/affection/faith)