You'll never get it all so don't expect your grill to look brand new. Spray the inside with a grill cleaner and wipe it down with paper towels. Again, you're never going to get it all, but wipe off as ...
WOW! What a mess! If the gunk won't come off with a brush, you can spray the inside down with some more oven-cleaner. In the case of a charcoal grill a final rinse after brushing the inside works ...