Oric wants "the aberration." We can infer from the Twoota tip that this is something he has been questing for for a long time, probably multiple cycles, possibly all cycles.
We've seen the term "aberration" in one other context; the classes "Aberrant Exile" and "Aberrant Thief."
What if the aberration Oric desires is the quality possessed by those members of the class?
Let's quickly review the inhabitants of the Warrens: Mercenaries and Illborn, who had their souls sucked out through a bendy straw as part of entering the Warrens. Siblings, who may or may not be related by blood but are certainly united under Oric. Angels, all those grey-skinned weirdos who are presumably the original inhabitants of the Warrens.
Let's now suppose that there's another broad category of Warrenites: the Aberrants. We know that they are a discrete group (Mili was an Aberrant Exile and lived in Underside; there must be something she was exiled from, and that would be the rest of the Aberrants.) We also know that they have thieves in their number, since there is a sidequest to catch them. We also know that they are not related to the other main groups in the Warrens; we've had extensive dealings with Mercs, Siblings, and the Angels, and the subject of the Aberrants never came up.
The common factor between the other three groups is that Oric controls them; if the Aberrants are completely separate, then perhaps Oric does not control them. The Warrens being what it is, I hypothesize that "the aberration" is whatever quality or power they possess that is able to keep them independent of Oric.
Following this line of thought, it could behoove us to speak with Polydectes on this subject, as he's the only other person we met who is explicitly subversive and hiding from the Angels (and by extension, Oric.) He might be an Aberrant himself, or he might have dealings with them. This can probably wait until the next time we're ready to upgrade somebody in the Dark Cathedral, however. In the short time, maybe we should see if Al knows more about Mili's past than he's revealed to Ciro.
Al: Think about Mili