You cannot use iTunes to transfer from iPod to computer (except for songs purchased from iTunes Store). By design, iTunes syncing is typically in one direction only, from iTunes library on computer to iPod. However, there are third-party methods and utilities that can transfer from iPod to computer. If you do an Internet search on something like "ipod transfer music," you should get some useful links, including an article by CNET on the topic.
Once your song files are on your Mac's drive, add them to your current iTunes library. After confirm your Mac has all songs, sync your iPod.