You can't transfer song files from iPod to computer using iTunes (except for songs purchased from the iTunes Store). However, there are third-party methods and utilities that can transfer from iPod to computer. If you do a Google search on something like "ipod transfer," you should get some links.
Once the songs files are on your computer, you can add them to your iTunes library.
This website walks you through step by step how to download the music from your ipod to either a Mac or a PC. For a PC, you will not need to download any software. I haven't tried the methods recommended for a Mac or for reformatting the ipod, but the method for the PC works.