Is it illegal to download songs off You Tube?

No, or, more accurately, the fact that it's on YouTube does not affect the legality one way or the other. It is illegal to download a song in violation of its copyright; where you get it is beside the point. So there are some songs that it's illegal to download from YouTube (or anywhere else with the exception of authorized stores you purchase the songs from), and songs that it's legal to download from YouTube (or anywhere else) because they're not copyrighted or because the copyright owner has chosen to allow it.