Why are there songs stuck on my new iphone 5?

So i just got a new phone for christmas. I have it all set up and connected to itunes. I have songs that i can't get off my phone, all the songs have the icloud sign next to it. But when i plug it into my itunes and check what is on the phone it says there are no songs on it.help! Some of the songs on my phone arent even in my library.

Try restoring the device (make backup first so you can retrieve your data)