Why do I have extra songs in my iPhone playlist that are not on my iTunes library?

After doing the iOS7 update (and iOS7.0.2) I decided to add my music to my phone (I never had music on it before).

I discovered that there were 20 very random and obscure broadway songs that were on my iPhone in addition to the 60 songs I just synced. They had the iCloud icon by them, unlike the songs I had just added.

After doing research I found that the broadway songs were technically "purchased" on iTunes although they are not songs I would have ever purchased- in fact I have never once purchased anything on iTunes. This isn't my worry though, I am assuming it must have been some random free download I did at some point?

I went to settings > music > and turned show all music off. This did NOT work for all of them and only solved the problem 80%. There are still 4 of the random song on my iPhone. They DO NOT show up in my iTunes library on my computer and don't even exist on my computer.

With the other songs I can left swip and delete but these 4 songs won't! Why won't these four songs left swipe?

I am going crazy and have tried restarting my phone, restarting iTunes, re-syncing, turning off the iCloud. NOTHING WORKS.

Please help. I am a normally a very smart and tech-savvy person and I cannot for the life of me figure this out. I don't want to wipe everything- which as a solution is a pretty weak solution.

Why won't certain songs left swipe to delete off my phone when I am in the music app?

Why do I have extra songs on my phone that don't appear on iTunes on my computer?

Where did these songs come from and how do I get rid of them?

Much thanks!