In a large skillet or wok, heat 2 tablespoons of vegetable oil over medium-high heat. Add the chicken strips and stir-fry for about 5-7 minutes, or until cooked through and golden. Remove the chicken from the pan and set it aside.
In the same skillet, add the remaining tablespoon of oil. Toss in the white parts of the green onions, garlic, and ginger. Sauté for about 30 seconds until fragrant. Then, add the cabbage, carrot, and celery. Stir-fry for another 3-4 minutes until the veggies are tender-crisp.
If you're using refrigerated Yaki Soba noodles, simply separate them with your hands and add them to the pan. If using dry Chow Mein noodles, cook them according to package instructions, drain, and then add them to the skillet.
In a bowl, combine the oyster sauce, soy sauce, sesame oil, rice vinegar, cornstarch, and brown sugar. Mix well until the cornstarch is dissolved.
Return the cooked chicken to the skillet, pour the sauce over the chicken and vegetables, and toss everything together. Stir-fry for another 2-3 minutes, allowing the sauce to coat the noodles and heat through.
If using, add the bean sprouts and toss them in for the last minute of cooking. Remove from heat and garnish with the green parts of the green onions.