Greyed out songs taking up memory?

Hey, various members of the Apple community.

This question has probably been asked before, but it's late, and I'm tired, and I've spent a good 2 hours trawling through the internet trying to find a simple explanation and fix for my problem.

Basically, the infamous Greyed Out Song thing has happened on my iPhone 5, and I wouldn't have a problem with this if it wasn't taking up memory. The way I can explain it is, I have two versions of nearly all the songs in my music folder- one that I can play, and one that's greyed out and yet still taking up memory. I don't want these greyed out songs there- why are they there, and how come I can't delete them?

I synced up my iPhone tonight trying to fix it (let's not even go into the fact it's refusing to sync an album as of right now...) and nothing has worked. Solutions? Explanations? Polite commands to go elsewhere? :/

Thanks anyway