In episode 4x16, Dr. Talter mentions that the Shapers were originally served by the djinn and efreet, and we know the Shapers also took elemental primordials as consorts, and that the celestials came later and were constructed using information from those primordials. Which is to say, I think Houses Einfasen and Cormoray may have started out as much more prominent under Tansul and perhaps got cast aside with the rise of celestials which would be interesting historically; and I think they are probably also historically extremely strongly allied given that shared primordial connection. I also think that Otto isn't bluffing; Einfasen (and Cormoray) have powers that are, I think, much, much harder to affect because they are tied to Aramán directly, whereas we know that extraplanar powers are subject to the status of that plane (Royce and Tachonis) and it's implied House Halovar specifically would have lost all sorcery were it not for Yanessa being the most opportunistic woman in the history of Aramán.
This involves a few major assumptions, ie, much of this is vibes so don't quote me, but: we know of eight noble sorcerous houses of Obridimia, five of which openly survived the Shapers' War and became known as the Sundered Houses. Three were presumed to have fallen: the royal House Obridai itself, and its two warrior houses, Kalystra and Memnari.
I have been operating under the assumption that these are the only noble sorcerous houses, especially because of the theories surrounding schools of magic. This means that the three rebel houses were the only rebel houses (ie, no rebel houses were believed fully destroyed in the Shapers' War), and specifically were on a slightly lower level than all five other houses (ie, there's Obridai at the top; Halovar, Tachonis, Kalystra, and Memnari at the second level; and then Cormoray, Einfasen, and Royce).
We know the power sources for Cormoray, Einfasen, and Royce (djinn, giants, and fae, respectively). Einfasen is explicitly stated to pre-date the Obridimian Empire and I suspect that the others do as well. I also suspect, given the knowledge of the Sea of Lachris, that House Tachonis also pre-dated Obridimia and simply joined its service as psychopomps; though it is possible that they were granted this connection by Tansul and merely knew of the Sea of Lachris because they have an inherent connection to the Tenebral Reaches. Also of note is that their connection seems to be specifically to the Tenebral Reaches, not to other realms of death, which is why they have grown in power since the Shapers' afterlives fell, and why they are trying to shut down all other options.
House Halovar's original power source is not clear. However, we know that Wick's power derives from his celestial ancestry, as a Clockwork Soul sorcerer. I've said elsewhere I suspect they were probably Divine Soul, and their deals with demons do not tie back into their sorcery, but this is not confirmed.
We know House Kalystra seems to have had stone-related abilities. One possibility for that is they had a connection to the dao as Cormoray did to the djinn (though, to be fair, Cormoray seems to also have efreet-related abilities and sometimes people refer to all the genies as djinn; I believe in the original Islamic folklore ifrit are demonic but grouped with jinn in some ways, so like. it's complicated). As Cormoray is looking into their quarries I suspect they were likely closely related.
Finally, we know Azune is a draconic sorcerer, and it is heavily implied that he derives his ancestry from a house believed to broken. Given that Luis has stated he is playing the multiclass as if it is one cohesive class, my guess is therefore Memnari.
