Cook celery and onion in the 1 tablespoon olive oil in a skillet until tender; cool slightly.
Combine egg, mayonnaise or salad dressing, dry mustard, garlic powder, onion powder, and ground red pepper in a mixing bowl. Add celery mixture, bread crumbs, crab meat, and the red and green sweet pepper. Mix well. Shape into 12 cakes.
Cook the crab cakes in the 3 tablespoons olive oil in a large skillet for 2 to 3 minutes on each side or until lightly browned. Serve with tartar sauce. Makes 8 appetizer servings or 4 main course servings.