I pretty much agree with Jon's definitions up there at the top. Now, a melody is a tune and a tune is a melody. This is why "tune" doesn't work for more elaborate compositions - they're more than just melody. You could call the "compositions" or "works."
"Song" works for words and a tune, because people sing songs. Of course, birdsongs don't have words (at least not as we know them) but birds sing them. But then you have someone singing scat or mouth music - is that a song because it's sung? Maybe technically, I don't know, but I probably wouldn't call it a song if someone's just vocalising the tune.
Carol, let me just add that I also enjoy your presence here, and you ask some darned good questions!