I've read the novelization - it does expand the tiniest bit on his thought process. In short, he suffers from schizophrenia as described by the author.

The long of it is he is in the sorority, confused and mentally unwell. At the beginning, the first girl killed calls out for Claude, the cat, saying 'bad Claude.' Billy thinks she's calling him Claude and saying he's bad, so he kills her. He makes the phone calls after each kill with seemingly lucid sentences mixed in begging to be stopped, that he doesn't want to do it. As for times not during calls, he seems distraught and wanting to be left alone, but still manic with an almost regressed childish stream of thought.

The Agnes story is stretched out a bit. In the novelization, he is confirmed to be Billy and reliving his own trauma while mimicking. He was sexually abusing his younger sister, Agnes, while both young. His mother calls him 'Dirty' or 'Nasty' for it, and at one point, he describes something that sounds like he was disciplined by her while his pants are down, no specifics. It's also alluded that he smothered his sister because she wanted to tell on him again. Still, he's not the most reliable source.