How do I get U2's album Age of Innocence taken off my phone? I've tried sending to trash, hiding the songs and nothing seems to help. Is there a way to get rid of this once and for all?

If you synced the album to your iPhone from your computer, you would use your computer to unsync the album.

See this --> Sync your iPhone, iPad, or iPod using your computer - Apple Support

This link explains how to sync content. To un-sync do the process in reverse.

I remember now. There was a time years ago when Apple downloaded the Album free to everyone. I found an old article you can try to get rid of it:

• Go to https://itunes.com/soi-remove.
• Click Remove Album to confirm you’d like to remove the album from your account.
• Sign in with the Apple ID and password you use to buy from the iTunes Store.
• You’ll see a confirmation message that the album has been removed from your account.
• If you downloaded the songs to iTunes on your Mac or PC or to the Music app on your iPhone, iPad or iPod touch, you’ll need to delete them manually.

If that doesn't work anymore, muguy is correct in that you should contact Apple Support directly.

If it really bothers you, contact Apple SUpport to have the album removed.