How can I clear unwanted music off of my iphone?

Solution 1:

These songs are iTunes purchases that are available for download but not currently on your iPhone. To hide these:

Settings > iTunes & App Store > Show All: Music = OFF

Solution 2:

You can delete them directly on your phone by sliding the song to the left on the songs list.

Solution 3:

If you have ever had icloud enabled, you will see all the music you ever purchased in itunes. Even if you turn icloud off, that music will persist in your music app. The only way I found to get rid of it was to go to the itunes store in itunes and hide all the unwanted music. Once I had done that, they finally disappeared.