I'm looking for a book read in the 1980s. The plot is that alien invaders have taken over earth. They have paranormal powers in that they can teleport. Their motives are unknown but most of them just choose a random human being to follow and irritate. I don't recall much about it except it s written in very funny way. One scene is when our protagonist asks his particular Martian about another guy who was hanging around the protagonists girl. He describes his final and adds that his rival "always wears suits". The Martian disappears and reappears, and informs theft that his description was wrong, as he did see a man with the hero's girl, but must be a different person, as "he can't be your rival, cause this guy wasnt in a suit, he was clad in nothing but a wrist watch!"
Any suggestions? Thanks!