Stephanie They were responsible. Near the end, it's mentioned they had to do it. They didn't explain the why, but it seems likely that without severing Shadow's only tie to family, Shadow never would have gone along with Wednesday's job offer.
Katy Thor is not in this novel, except as a throwaway reference as a dead god. Loki and Wednesday/Odin were responsible for the accident, yes. During the confrontation at the battle, they heavily, heavily imply it to Shadow, if not state it outright.