There was a passage in TTT that I thought explained a lot of what is going on with the characters in this book but especially Serwe:
One night during the infancy of the Holy War—and for reasons Cnaiür could no longer recall—the sorcerer had taken a crude parchment map of the Three Seas and pressed it flat over a copper laver filled with water. He had poked holes of varying sizes throughout the parchment, and when he held his oil lantern high to complement the firelight, little beads of water glinted across the tanned landscape. Each man, he explained, was a kind of hole in existence, a point where the Outside penetrated the world. He tapped one of the beads with his finger. It broke, staining the surrounding parchment. When the trials of the world broke men, he explained, the Outside leaked into the world.
This, he had said, was madness.
...
The bead had been broken—there could be no doubt of that. According to the sorcerer, madness all came down to the question of origins. If the divine possessed him, he would be some kind of visionary or prophet. If the demonic …
The sorcerer’s demonstration seemed indisputable. It accorded with his nagging intuitions. It explained, among other things, the strange affinities between madness and insight—why the soothsayers of one age could be the bedlamites of another. The problem, of course, was the Dûnyain.
He contradicted all of it.
So this is why Achamian is having the distorted dreams, Cnaiur is near unkillable, Saubon fought off the Coyauri single-handedly at Mengedda, and Kellhus begins hearing voices and seeing halos after the Circumfixion.
The general impression I got on the reread was that Serwe's captivity with Cnaiur was the straw that broke the camels back - the reason she could be so deluded as to think her child is Kellhus' is because she has actually gone insane.
Dread.
Tyrannizing her days. Stalking her sleep. Dread that made her thoughts skitter, flit from terror to terror, that made her bowels quail, her hands perpetually shake, her face utterly slack for fear that one crimped muscle might cause the whole to collapse.
...
None of this is happening, she thought. No one suffered like this. Not really.
She feared she might vomit for dread.
There's also a passage illustrating how all of this had built up to this collapse:
Her father, pulling her half-naked from her blankets, thrusting her into the callous arms of a stranger. “You belong to these men now, Serwë. May our Gods watch over you.”
Peristus, looking up from his scrolls, frowning with amused incredulity. “Perhaps, Serwë, you’ve forgotten what you are. Give me your hand, child.”The Gaunum idols, leering at her with faces of stone. Sneering silence.
Panteruth, wiping her spit from his face, drawing his knife. “The track you follow is narrow, bitch, and you know it not . . . I will show you.”
Cnaiür, clenching her wrists tighter than any manacles. “Mend yourself to my will, girl. Utterly. I will tolerate no remainder. I will stamp out all that does not submit.”
So it would seem Serwe's other-worldliness stems from her mental state, that the awe others felt around her is legitimate. Regarding the "origins" as Cnaiur put it, whether she was possessed by the divine or demonic, I would say divine, as she finally began to mean something as she always wished, rising to a prominent place, desired by others, and possibly helping Kellhus' shrial knights prophecy come true at Mengedda. This puts into perspective why, after Kellhus sacrifices her, he shortly thereafter has visions of the No-God, suggesting the origins of his possession are demonic.
Of course, as Cnaiur notes, Kellhus' mastery of men contradicts the possibility of free will and meaning in Earwa. Perhaps the way these individuals seem different to others is just the spark of madness in their eye or the witness' own delusion. But if there is some system of the Outside leaking in, it seems this would explain it.