Bring a large pot of water to a rolling boil; cook noodles until al dente, about 7-9 minutes. Drain and keep hot.
Meanwhile, combine soy sauce, oyster sauce, sugar, and sesame oil in a small bowl; whisk to combine and set aside.
Heat 1 tablespoon oil over medium-high heat in a wok or large, non-stick skillet. Once hot, add chicken and cook 3-4 minutes, turn and continue to cook until cooked through, about 2-3 minutes longer. Transfer to a plate.
Return skillet to heat and reduce heat to medium-low. Add remaining 1 tablespoon oil in skillet. Once hot, add celery and saute 3 minutes. Add cabbage and saute 2 minutes, then add carrots, green onions, ginger, and garlic; saute 1-2 minutes longer, until veggies are all crisp tender.
Toss in noodles and chicken then pour soy sauce mixture over top and toss to coat. Cook 1-2 minutes to heat and allow noodles to absorb the sauce. Serve hot.