3 exercises that will enhance your grappling and striking -
Deadlift - both speed and heavy
Clean and Jerk - both speed and heavy
BW Pullups
Work your core, your obliques and your abs. Do plyometrics with a medicine ball, train abs heavy with weight, rotations, twists, saxon bends etc. Work your shoulder rotators and hamstrings, because they can very easily get injured.
When I was on judo team on my schools team, I often had the edge because I had stronger core, thanks to deadlifts, strong lats and explosion to either get out after getting pinned, or shoot for a take down. Ofcourse the best way to enhance your striking and grappling is to actually practice it. I've tapped 250 lb men because I have been lifting heavy in deadlift and other power moves. However I've been owned by a little 130 lb man. I was so tired that I attempted to actually benchpress him off of me. But the exercises I listed give you an edge if you are fighting someone with similar skill level.