Tracks listed under "Manually Added Songs" continue to re-appear
When you delete songs on an iPod (or other iOS device), they get copied back the next time you sync with iTunes. This makes no sense, of course, but that's the way it works. (It correctly does not re-sync apps you delete, most of the time.) The only way around it is to un-sync the tracks - make sure they are not selected in the Music tab, or are not in any playlists, or uncheck the tracks and choose the Only sync checked songs and videos options. Or you can manually sync music to the iOS device, but that may not be what you want.