I have the exact same experience. It may even, unintentionally, be the _reason_ I don't listen to Pop music. It's generally not even a whole song - usually not even the chorus. I'll get a 2-4 second loop in my head of some insignificant section of a crappy song for 2 or 3 whole days.
Like you, it will sometimes start when I'm sleeping. I won't remember much of the dream, but the song is still there, echoing as it was in whatever setting my dream took place.
Like you, it will sometimes start when I'm sleeping. I won't remember much of the dream, but the song is still there, echoing as it was in whatever setting my dream took place.