I'm trying to find an old program that's no longer available on the Apple Store but used to be on my ipod. If I restore from an old back-up, will the latest back-up and all the data I have saved on my apps still be there?
No. The backup that iTunes makes does not included synced media like apps and music. The only way to get an older version of an app is that if you saved them like as part of a computer file backup.
I mean restoring my ipod, not my itunes. If I restore the back-up from 2010 on my ipod, will the back-ups I made after that still be there?
The app data is in the iPod backup that iTunes makes. However, the app itself is not in the backup.
In order to have the app data restored, the app has to be in the iTunes library on the computer on which you restore the iPod.
So I guess that applies to TV shows as well?
Correct. The iPod backup that iTunes makes does not include synced media like app, music, synced moves and TV shows. For what the backup contains see:
iTunes: About iOS backups
Retrieving data ...