Why do deleted songs keep returning?

When in Itunes I'm trying to delete songs from my Iphone. When I click on the music tab I see boxes with Playlist, Artists, Genres, and Albums. I can also see a list of some songs I added manually. In certain boxes I can click to add or remove entire albums, however some songs I want to remove individually. I try to right click, but no delete option is available.

So I go into my Iphone and delete them directly from the phone, however when I re-synch all the deleted songs are back again.

Very frustrating!

Please help!