jckinnick -
To completely delete the songs from your account you apparently need to be an iTunes match subscriber. Paying $24.99 for the ability to delete free songs I don't want didn't appeal to me.
Hiding them on my account in iTunes didn't work (aggravating).
I made sure "show all" and iTunes Match is turned off under
settings > music
and
settings > iTunes & App Store.
And deleted every song from my iPhone. You may be able to swipe to remove individual songs, but I couldn't when I first tried so I went the settings > general > usage > music route. If you can swipe to remove individual songs from your iPhone try that method instead.
Again, if show all is on in any of those places I mentioned, you will still see songs you do not want available on your iPhone.