Combine oil, vinegar, lemon juice, salt, lemon pepper, tarragon, and garlic powder; stir until well blended. Cover and refrigerate overnight.
Position crabs securely in a wire grilling basket. Place crabs, back side down, 4 inches from hot coals. Grill 10 minutes, basting frequently with sauce. Turn basket with crabs, and grill an additional 5 minutes. Baste frequently with remaining sauce. Serve immediately.