What format are the songs in?

Have you made iTunes your default player? If you want iTunes to play your downloads, disable the LW player & make iTunes the default.
Changing default player

If you want to add songs to your iPod, first you have to add them to the iTunes library. It's no good trying to add the songs from within the LW playlist that you see in iTunes ("your name's LimeWire Tunes")...you'll have to add things from your LW saved folder. Read through the sticky below, it's got a lot of info!
Transferring music to iPod & iTunes