If I'm understanding you correctly try this:
1. Download the latest version of itunes and install it on each computer. You'll need an internet connection or save the install file to a jumpdrive. http://www.apple.com/itunes/download/
2. Fill your HD with all of the music files you want to use in itunes. Use itunes to upload the music from the portable HD. http://support.apple.com/kb/HT1473
3. It sounds like you want to store the music only on an external HD. In that case you need to have the HD plugged in while listening to music or updating your ipod.
4. Even though itunes will list all of your songs it can't play them without the original uploaded source files being available.