IF THE MATERIAL IS GLASS OR METAL and it is quick and easy to clean, great: clean them then recycle accordingly. If it's hard to clean: chuck it. 

Paper cannot be cleaned of grease. Put in the waste bin.

Oily plastic should also be tossed. In our opinion, it's not worth the water, soap, and effort to clean these items because recycling rates of plastic are so low. Same goes for tetrapaks and other food cartons.