As a kid in West Africa I had 2 tunes that I didn't know what they were that would get stuck in my head. Turned out many, many years later to be the whistling from Andy Mayberry (which I didn't even remember ever watching, we didn't have TV) and Food Around The Corner For Me from, I think, Bugs Bunny.
I do find that if I have a song stuch it tends to be something I don't know all of, because if I can sing it all the way through it tends to get rid of it (and sometimes substitute the next one on the album). If I can't sing it all the way through, I'm stuck.