Ultimately, all of your songs should be in your iTunes library, not only on an iPod. iPods get broken and lost. By design, iTunes cannot transfer song files from iPod to computer (except for songs purchased from the iTunes Store). However, Apple does not prevent it. 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 link including an article by CNET on the topic.
Once the iPod's song files are on your computer, add them to your iTunes library. After confirming you have all of your songs, make whatever sound adjustments are needed, and sync your iPod. Going forward, back up your complete iTunes library data and use the backup on new computer, if old one fails.