Something Weird (1967)

Cronin Mitchell is an average guy whose face is disfigured by a falling electrical power line in which he somehow acquires the gift/curse of strange psychic powers. After withdrawing from public life, 'Mitch' makes a living as a fortune teller when he's approached by an ugly hag who offers to restore his good looks if he becomes her lover. Mitch reluctantly agrees, and although his face is restored, people around him see his lover as an attractive young woman named Ellen. When news of Mitch's psychic powers leak out, he goes on the road with Ellen from city to city and town to town helping people solve crimes. After expelling a ghost from a funeral home, Mitch and Ellen are sent to a small Illinois town to find the identity of a serial killer. But the government sends along a crackpot psychiatrist/playboy, named Dr. Alex Jordan, to oversee the case and possibly debunk Mitch's psychic abilities. When Dr. Jordan turns his sights on Ellen and plots to steal her away from Mitch, she goes to great efforts to prevent that from happening while helping Mitch try to find the serial killer.