Cook the noodles according to package directions, omitting salt and fat.
Combine onions and next 5 ingredients (through garlic) in a small bowl.
Bring 8 cups water to a boil in a large saucepan. Add cauliflower, carrot, and broccoli; cook 2 minutes. Add squash, and cook 1 minute. Drain vegetables in a colander. Combine noodles, onion mixture, and vegetables in a large bowl; toss to coat.