I got a 2008 iPodNano and a 6S+ iPhone, all of my songs are in iTunes on my iMac, i sync them on the Nano and i listen to music when in the car or away from home. Can i sync those songs to my iPhone (iOS9) and listen to music from it too?
Yes providing that you have enough storage space to accommodate your library. If not you can sync playlists. If you purchased any of your music from itunes it will be available to stream over wifi or cellular automatically.
You also have the option of signing up for iTunes Match or Apple Music which would allow you to upload your entire music collection and then you would be able to stream it over wifi or cellular on your iPhone.
Another option which is free is to use google music. They allow you to upload all of your music from your computer into their cloud service. If you download the play music app on your phone you can then stream it.
You have a lot of options, not including other apps/ services.