Combine olive oil, onion, cheese, basil, mustard, orégano, sugar, salt, and pepper in container of an electric blender; process 30 seconds. Add vinegar and lemon juice; process an additional 30 seconds.
Place fish in a wire grilling basket; grill over hot coals 10 minutes on each side or until fish flakes easily when tested with a fork. Baste frequently with prepared sauce.
Remove fish to a warm serving platter; garnish with lemon wedges.