You can delete them off your phone, but if you don't edit your library in iTunes, it'll show back up every time you sync. That's.. kind of the point of syncing.
Then...what's...the point of...being able to...delete them from your phone?
I think I figured out how to solve the problem:
1) Check "Sync only checked songs and videos" and 2) "manually manage music and videos."
Then what you'll have to do is uncheck all the songs in your itunes library and make sure that all future songs you add to your library are unchecked. This won't erase them during your next sync but if you delete them on your device, since they aren't checked in itunes, when you resync they won't be transferred. You can add new, unchecked songs by clicking and dragging them into your phone or adding them to a playlist like before.
So to test this (I already have, but please test it with just one album): do 1 and 2. Find an album in itunes and uncheck all the songs. Sync. Make sure album is still on your phone (it should be). Delete that album from your phone. Sync. The album should not reappear.
If you try this then please do it with just one album to test just to make sure. I've tried it and it seems to work.