I keep my music files on an external drive, once I have added the songs to my iPod Classic are they saved on my computer as well? I don’t have a lot of space on my computer and transferring songs has left me with even less space on my computer.
howapple - hello
Ideally you would have things set up so that starting iTunes with the external offline doesn't cause you any problems, and you would have a backup of your iTunes library and other important data on another drive. Syncing your iPod has no impact on the files on your computer. You add songs to your iTunes library. Whether or not you then add them to the iPod won't change how much storage is being used on the internal and external drives.
Check under iTunes (Mac) or Edit (Win) > Preferences > Advanced and look at the location of the media folder. Is where you think it should be on the external drive or has it been reset to the internal drive? If it is wrong change it back to your preferred location, consolidate the library (File > Library > Consolidate Files), then delete the now redundant media folder on the internal drive.