I have a subletter in my apartment who's contract runs out in January. She has already left the premises leaving her key and a note that said "seeya". She did not leave her check for the previous months utilities that she owed, and she also left several items of furniture in the room that she occupied.

I have a signed contract that states she is to pay rent and utilities until January 1st. It does not specifically state that she can't leave furniture in the apartment.

What can I do at this point legally to get rid of the furniture and receive payment for the utilities?

Sell the furniture to pay for the utilities. Haha.

Since she turned over the keys she has abandoned the furniture. You can sell it or throw it out. To recover any monies owed you need to sue her.