You may need to turn off itunes match on your phone in settings. You should also be able to swipe across a selected song, artist, or album that you do not want and see a red delete button appear. If you can not get that to work, you can go into settings and delete all your music but you'll have to re sync all your music you want.
Tuen off iTunes Match on your phone: go to settings/iTunes & app stores/select iTunes Match off.
To delete all music completely: go to settings/general/usage/music (once it loads the parameters) swipe across and press delete.