On the Exxon Valdez spill, the best degreaser they could find for crude oil was Dawn Dishsoap. That was out of everything available to them. After you get the majority of the gunk off, try ENGINE BRITE by GUNK. It comes in a white can and you can get it at most auto parts stores or Costco. Follow the directions.
Then, use the Dawn one more time to get any residual off.
As far as the grill itself, many new ones are porcelan, and you can put them in your self cleaning oven the next time you clean it. Comes out like new, but you want to get as much as you can off of it first, or it'll stink up the house.