Assuming that you have purchased the songs and they are not part of an Apple Music subscription, have you downloaded your purchases to your iTunes Library and do the songs play in your library?
If they are downloaded (and play), and you use Sync to manage your iPod, have you included them in items to be synchronised with the iPod? For example, if you Sync selected playlists, artist, albums and genres, the new songs need to be included in one of the categories that you use to sync with the iPod.
If you use Manually Manage rather than Sync, you need to drag the new songs onto the iPod.