My roommate has moved out, but all of his stuff is still in the apartment. I am the *only* one on the lease. My landlord knew he was their and not legally on the lease. He won't answer my phone calls, and has not called me back. Can I remove his things myself or is this illegal? Is there a time of how long they have to be left in my apartment before I can do anything?

I would have to say if they left it there and you cannot get a hold of them, I think you could get rid of it.

In landlord-tenant law language "moving out" means
1. returning keys,
2. giving a letter that says "I have vacated",
3. etc.

... without something from the person that moved indicating "I have vacated" then you can only go by what's "reasonable". To me, reasonable would be taking pictures, moving the stuff to storage and waiting a couple to a few months... then either throwing it away, keeping it or selling it as your discretion.

In most jurisdictions property is assumed to be abandoned after a period of 180 days. Making a good faith effort to contact him, which you have done, helps as well.