I removed some songs from my directory, how do I tell iTunes to remove them from my library?
iTunes has no functionality to actually scan for missing songs from it's library. If you want to delete Music, you need to do it from within iTunes, and not the other way around. It can however identify missing files which normally appear with an ! mark next to their names. These can simply just be deleted out of the library manually.

There are some 3rd Party options to try and do this automatically:


AppleScript Scan Missing is an AppleScript solution if your using a Mac or this AppleScript from MacOSXHints. 
For Windows you can use the iTunes Library Scanner mentioned in this iLife article.


Once you have removed the songs from the iTunes library, they will be removed of your iPod the next time it synchronizes.