How to get rid of extra songs on my Iphone?

I recently upgraded to the Iphone 5s from the 4. However, when I set up the phone, every single song I had ever purchased has returned even if I have fully deleted them from my computer. As a result, I have 100s of extra songs and no room. How do I get rid of them? There are also extra movies and tv shows that I had deleted awhile ago

Added (1). Simon, I tried that. I had to download the song first, then delete it. But when I "delete" it, the song is still on the phone. It just has to redownload. I want the songs to not appear in my library anymore, not to simply be not downloaded.

Okay this is very simple. Open music and go into where all your songs are displayed. Decide which song you want to delete and slide your finger from left to right on top of the song you wish to delete. A small red button which says delete should appear, tap on that.

I think you can use iTunes to do that.
Download all your music to your iTunes and select the one you want to sync with you iPhone.
It's easy.

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