BOZ said:
Do we know anything more about the early origins of the archomentals, other than Tharizdun may have spawned them?
Not really. I had the idea that they were something like stupendously powerful grue. Grue, as you know, are created from evil spells being cast in the elemental planes, forming around cores of vile magic. The Elemental Princes of Evil formed similarly from the keys to Tharizdun's prison.
Not official, of course.
I won't be using Bwimb (just the original 5), though I may toss his/her name around a bit. Of course, now that I think of it, what sort of relationship did the 5 main evil archomentals have with the lesser folks (like Ehkahk and Chilimba)?
Bwimb was the most powerful known of the ooze paraelementals. He was apparently evil (his "daughter," Bwimb II, certainly is, and has an alliance with Juiblex), and really not so different from, say, Cryonax, who is the most powerful known of the ice paraelementals.
The others aren't elementals, and thus can't really be called archomentals. Ehkahk is an unusually brilliant smoke mephit. Chilimba is a magma mephit/magma paraelemental crossbreed trained by the baatezu.
The 1st edition
Manual of the Planes defined archomentals the best, I think. Broadly, they're the second tier of elemental power, after the elemental rulers Akadi, Grumbar, Istishia, and Kossuth. On most planes there are more than just two of them - they're of various alignments and beliefs. There's no reason there couldn't be Elemental Princes of Law and Chaos, for example.
I'd say they were somewhere between the elemental rulers and the primal elementals in power (of that they're simply more intelligent versions of the primal elementals). In 1e, they were equivalent to demigods.
Do we know if these 5 have any established relationships with other gods? What about archfiends?
No, just Tharizdun I think. Bwimb II has an alliance with Juiblex, as I mentioned.
Do these 5 archomentals have any other notable servants, or creations, artifacts, notable allies? Who are their enemies (besides each other), and do we know how these relationships formed?
Imix's greatest foe is Olhydra, with his son Zaaman Rul a distant second. Ogremoch's greatest foe is Sunnis. Olhydra has alliances among the hezrou tanar'ri. Her greatest foe is Imix, and she completely ignores Ben-hadar. Yan-C-Bin is engaged in a subtle cold war against Chan (the two have never actually met, but compete in information-gathering and spying). Ogremoch and Yan-C-Bin are enemies, but their hatred is not as vehement as Imix's and Olhydra's.
The origin of these disputes is pretty obvious: it's all about natural elemental and moral antipathies.
Cryonax's primary rival is Albrathanilar, greatest of the white dragons of the paraplane of Ice. Albrathanilar is also a powerful and crafty wizard, a worthy foe of the archomental prince. They are rivals simply because they're the two most powerful individuals on the plane, and they have incompatible goals.
The four elemental rulers are distant and removed from the archomentals and their petty squabbles.
Chilimba studied torture under a powerful pit fiend. Imix is served by a pit fiend general called Asgeroth.
There are a few named servants of the various archomentals. A dwarven warrior/priest called Kaylef once served Ogremoch, but he was found wanting and cast aside, though he is still filled with great power. Imix has his general Asgeroth. Olhydra is served by a trio of sea hags called the Blue Coven.
I'm not aware of any other interactions between archomentals and gods, but a look at a list of which gods live on what plane might give you some ideas. Oh, wait: there's a disagreement between Olhydra and Cegilune over the matter of the Blue Coven.
That's interesting.

Is their involvement in the setting more of an "oh, by the way" mentioning, or do they have more direct involvement and interests therein? I may not use the AQ stuff much at all, but it might just be interesting for me to know.
Mostly "oh, by the way." Imix's shrine in the City of Brass is called the Mosque of Blistering Atonement, and it's briefly described in
Secrets of the Lamp. Exactly which archomental the djinn stole their Court of Ice and Steel from is a bit muddled. The text says "Inix, Princess of Elemental Evil," but as Imix is male and is unlikely to build with ice, Wolfgang Baur probably meant Olhydra, the only Princess of Elemental Evil there is other than Bwimb II, who didn't exist yet (and she's more properly a baroness). On the other hand, Yan-C-Bin (who shares a plane with the djinn) and Cryonax (who is more associated with ice than any of them) are also candidates.
The monster sheet on ildriss (air grue) says they're all servants or spies of Yan-C-Bin. There are also good ildriss, called "fog ildriss," who have abandoned Yan-C-Bin's worship.