Q: can't find album on ipod

but they show up when I connect it to a tablet or PC

Are you looking at content on the iPod, as shown in iTunes on the computer when you select iPod in iTunes window?  Or are you saying the album appears in your iTunes music library, but not on your iPod?

So, you're saying there are songs on your iPod that are not in your current iTunes library (on the computer)?  If so...

First, if you believe those songs should be on your computer, you can try doing a general search (using Windows) for the song files.  Search on the name of a song (or a key word in song's name).  If you find one of the song files still stored on your computer, you may find others along the same file path.

If you don't find those song files on your computer, you'll need to off-load them from the iPod, and add them to your computer's iTunes library, so that it is complete.  iTunes syncing is generally in one direction only, from iTunes library to iPod.  You cannot use iTunes to transfer song files from iPod to computer (except for songs purchased from iTunes Store).  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 music transfer," you should get some links.

After your iTunes library is complete, you may want to use automatic syncing to keep your iPod "in sync" with your iTunes library.  Then you'll not have a case of the iPod having songs that are not in your iTunes library.  And back up your computer's complete iTunes library data (along with the rest of your user data) to protect against your computer or its drive failing.

If your problem is not what I guessed, or you have questions about the above, please post back.

NOTE:  Songs purchased from the iTunes Store can be downloaded again at no cost

Download your past purchases - Apple Support