Well, I think my info is correct, and everything on your old iPod is already in your iTunes library. So, you don't have to do anything with your old iPod. You just asked the "wrong" question... 🙂
I think you need to set up automatic syncing for the iPod touch. "Syncing" doesn't do that much if nothing is set up to sync.
Select the iPod touch in iTunes. There is a row of "tabs" (starting with Summary). Click on Music there. This is the Music tab, where you tell iTunes how to sync the iPod with songs. Sync Music is checkmarked for automatic syncing of songs.
If your entire iTunes music library can fit on the iPod touch, you can choose to sync Entire music library. Then, everything in your iTunes music library is synced to the iPod touch. Your old iPod is probably set up this way. However, an iPod touch does a lot more, such as run apps and play videos nicely, so even if it fits, you may not want to sync your entire iTunes music library, to have space for those other things.
Therefore, you can choose to sync Selected playlists, artists, albums, and genres. Create your selection of songs below. For example, if you want to keep it simple, create a new regular playlist in iTunes and call it something like "iPod songs." Put ALL songs you want on the iPod on that playlist. Back on the Music tab, find and checkmark that new playlist under Playlists.
NOTE: You can set up automatic syncing for the other types of iTunes media, such as Podcasts, Movies, TV Shows, Books, etc., on the other tabs with those names.
When you click Apply, your selections on the Music tab (and other tabs) sync to the iPod, replacing its current content. Going forward, any library changes that are related to the settings on the Music tab (and other tabs) sync automatically when you connect the iPod, or when you click Sync. So, if there is a playlist with your "iPod songs," you can just update that playlist (add and remove songs) whenever you want, even when the iPod touch is not connected; iTunes automatically updates the iPod with the same changes at the next opportunity.