This sync issue is nuts! I just upgraded my iTunes to the most recent version and still no resolve with the sync issues I was having either. From what I can tell, if I buy music from the iTunes store, those songs seem to sync. If I import a CD or copy a song from say Youtube and bring it into my iTunes library, those songs will NOT sync. Prior to updating iTunes or iOS 7 on my phone, I could do what I cannot do for years now. I can clearly see the songs listed in my iTunes library, hook my phone up to the computer via the USB cable and go through the entire sync process and look at my phone when its completed and no changes have been made with songs I manually added to my library.
I wish there was a way you could manually add songs to your phone instead of having to do a sync.
Also to those that say iTunes is telling you, you don't have enough space on your phone. One common thing to keep in mind to free up space is to delete your text messages! I recently deleted text messages for one of my contacts and believe it or not, it freed up about 4.5gb of space on my phone!
I have an old iPod Touch without a camera and its using OSX 5.1.1. I tried to update to the most recent OSX but it keeps saying its up to date. Well anyway, I am going to try and use that and see if that will sync and have my imported music show up on that device.