How do I find songs in my iTunes library that aren’t associated with my Apple ID? I get messages when syncing my iPod that tell me that a song cannot be copied because I am not authorised to play them.

Is there a quick way to find all songs that are like this and delete them?
First, why not authorise your computer? Store → Authorise This Computer… and log in.

Whilst you can't distinguish between songs for an authorised Apple ID and an unauthorised Apple ID, you can create a smart playlist that shows Purchased songs.