My thoughts...
Pact magic - Suel
Shadow Magic - Rhenee
True Name - Oeridian
Incarnum - Flan
Warlock Incantations Ur-Flan
Psionics - Baklunish
Anyone else have opinions?
Oeridians traditionally use big, flashy war magic. Evocation would be their school of choice. Such is one of the primary reasons they dominated the Flaneass in the migrations. As Erythnul is known for changing form, transmutation may be popular among the more savage Oeridians.
Suel would seem to use enchantments and illusions. They have large slave populations to control and also seem fascinated with lies and deception.
Baklunes seem affiliated with divinations, what with their focus on fate.
Ur-Flan undoubtedly use necromancy. I like to think of them as solely devoted to Nerull.
Baklunes, and Oeridians to a lesser extent, use psionics, judging by their gods.
Being pushed into marginal lands, Flan may have turned their magical focus toward abjuration for protection. I also think of them as favoring transmutation so they can be more like the nature they adore.
Rhennee seem like they would favor illusions.
True Name would probably be either Ur-Flan or Suel. Perhaps both. They are the two cultures most likely to "play god" with it.
Shadow Magic is certainly Suel. They're devious enough to develop a liking for it, even though one might argue that - given Xan Yae portfolio - it should be Baklunish as well.
Incarnum should be viewed with horror by most Oerthian cultures, even evil ones. Using souls for power is something the Ur-Flan would probably do but I prefer to keep their focus on necromancy and fiend-summoning.
The Baklundish
Arcane: big on Elemental forces, Summonings, and other planar beings. Pact magic would be a good fit.
Divine: Solid pantheistic outlook, the Baklundish people worship all their gods as one group, turning their specific prayers to whichever diety oversees what is being asked about (very Hinduish)
Psionics: one of the few peoples in Oerth with the gift of Psionics (which they were given by Xan Yae) and psionics has a very monastic order to it since it is only taught in a few of the monestaries of Xan Yae and Zouken.
The Suel
Arcane: a dark and cruel people, practicing all of the schools of magic but being especially good with the necromatic arts (their goddess of magic is also thier goddess of death). Dark, secretive and Machiavellian, shadow magics would fit well here along with normal wizardry.
Divine: Polytheistic outlook, the Suel tend to worship one specific diety in their pantheon and send all their prayers to that god or goddess (more greek/roman in flavor). Strife between the faiths is not uncommon.
Psionics: rare, but some knowledge of it, stolen from the Baklundish before the twin cataclysms. Suel psionics is very hidden and information about it is often inaccurate, since it is most often used in espionage and assassinations.
The Oeridian
Arcane: they use their magics to conquer others. Most of their magics are gears toward combat, and enhancing combat effectiveness. Warmages and combat specialized mages abound.
Divine: Evolving. The Oeridian pantheon started very basically, with Pelor, Beory, and the four seasonal gods. Over time and with interaction with the other races the oeridian pantheon has developed into a more polytheistic system.
Psionics: Actively hunted. The leaders of the Oeridians understand the arcane and divine and know how to use it and those that wield it as their tools, but they do not understand psionics and see it as a possible source of sedition.
The Flan
Arcane: the Flan had a horrible start with magic, with one of their first mages being Vecna and most of the early Ur-Flan empires devistating themselves with the misuse of magic. The current Flan still tend to avoid arcane magics and have no particular 'flavor'. Those that do go into it often follow the path of those before and delve into necromancy or perhaps develop as warlocks.
Divine: very Druidically based, with unfortunate dealings with dark dieties and he who must not be named.
Psionics: almost none, and no developed tradition.
The Rhennee
Arcane: the Rhennee excell in charms and illusions, and to a lesser extent divinations.
Divine: an alien people, the Rhennee have been forced to accept what gods they could find here on Oerth and worship the more common dieties of any of the pantheons.
Psionics: almost none, and no developed tradition.
Shadow Magic - The Valley of the Mage, the ancient Suel spellcaster Xodast
True Name - Flan
Incarnum - Olman
Warlock Incantations - The ancient Suel house Malhel, Horned Society
Psionics - Worshippers of Xan Yae and Zuoken, St. Cuthbert's Order of the Stars, worshippers of Delleb, worshippers of Syrul or Lydia, monks in the Far West
The Oeridian
Divine: Evolving. The Oeridian pantheon started very basically, with Pelor, Beory, and the four seasonal gods. Over time and with interaction with the other races the oeridian pantheon has developed into a more polytheistic system.
I would be very interested in knowing which source identified Beory and Pelor as Oeridian gods when they have always been presented as Flan
We know from Holian's stuff in the LGJ (Death Knights) that Solan was the Oerid name for Pelor. Pelor also seems to have been known to the Bakluni (if that Bakluni pantheon thread over and Canonfire is to be believed) and we know that the Bakluni and Oerids shared a lot of history in the past.
Finally, as the Oerids basically conquered the Flanaess (the various Suel enclaves in Keoland, Urnst, Rhizia notwithstanding) and we find that Beory, Pelor, Rao, Nerull etc are still considered major gods - then they've either been really successfully absorbed by the Oerids and/or the Oerids knew them already by other names. It comes back to the origin of the Common gods in the various gods lists. Some are gods that may have been common to the various cultures before they mingled during the Migrations; others will have been absorbed and adopted by the common Flanaessi culture after the Migrations.
P.