I find that the scouring side of a blue ("non-scratch") kitchen sponge, with water and dish detergent and lots of elbow grease, is effective, but it does require lots of elbow grease and I'm wondering if there's an easier way.  
Whenever practically possible, wrap your food in aluminium/kitchen foil. It will prevent a lot of cleaning later on. And it will preserve all the flavors and juices.    And as others have suggested, I find it easy to clean with a piece of dry or wet tissue and then water while it is still warm. 