Well, I have looked for you and if you have them on your playlists there is an edit button which if you press, you can delete all of them. This can only be done with playlists you have created not the iTunes playlists like recently added or top 25.
I don't want to delete any but I'm sure it's a one touch of each song to delete. Sorry if you haven't found any other way yet. We do try to help but remember we aren't Apple employees who know everything, we are members who are trying to help you, please be a little more respectful if our suggestions aren't helping you!
I had loads of problems with the music app when I updated so I do understand your frustration. I deleted my song library three times before it worked and my songs were corrupted and were there but not playing at all just skipping. Let us know if you find another way to delete. There are other threads on this topic, search is your friend.
Sent from my one and only original iPad using iPF