Combine dashi, soy sauce, mirin, and sugar in a bowl and set aside.
Soak noodles in boiling water for 1 minute. Drain and rinse under cold water.
Heat 2 tablespoons canola oil; cook and stir beef in the hot oil until no longer pink, 2 to 3 minutes. Drain and set aside.
Heat 1 tablespoon canola oil in the skillet; cook and stir onion, celery, carrot, and mushrooms until softened, about 4 minutes. Stir in green onions, and dashi mixture, noodles, beef, and tofu. Bring to a simmer. Divide hot sukiyaki among four bowls and serve.