Mix all the sauce ingredients in a bowl and set aside.
Cook the noodles according to package directions.
Cut the chicken into small, thin slices. Heat a wok on medium-high heat. Add oil and cook chicken until lightly browned on all sides. Remove from the wok and set aside. Add in cabbage, celery, and carrots and cook for about 2 minutes or until vegetables are softened, stirring often.
Stir in the sauce and cook until thickened. Add the chicken and noodles to the wok and toss to coat all the ingredients with the sauce. Garnish with the green onions.