Just to add.... make sure you are not in a playlist, when trying to delete a song.
I couldn't understand why it just wouldn't delete a track off my iTunes, then found I was in the "recently added" playlist. So moved out of the playlist by clicking on MUSIC then located the track and deleted as the post above detailed.
The next time you connect your iPod to the computer it will synch with your iTunes library. And as the track has been removed from the library the iPod will be an exact copy.
PC