Bring a large pot of water to a rolling boil. Add the chow mein noodles and cook until very al dente—slightly under the package time (about 2½ to 3 minutes for many brands). Drain and rinse under cold water to stop the cooking, then set aside.

In a medium bowl, whisk together the soy sauce, oyster sauce, sesame oil, and water until smooth and combined.

Place the sliced chicken in a bowl and toss with 1½ tablespoons of the prepared sauce, the cornstarch, and salt so the pieces are evenly coated.

Heat 1½ tablespoons of vegetable oil in a 12-inch nonstick skillet over medium-high heat until shimmering. Add the chicken and cook, stirring often, until just cooked through, about 3 minutes. Transfer the chicken to a plate.

Add the remaining 1/4 cup vegetable oil to the skillet. Add the cabbage, celery, carrots, scallions, and garlic, stirring frequently until the vegetables soften and begin to brown, about 8 minutes.

Return the cooked chicken and noodles to the skillet, pour in the remaining sauce, and toss or stir-fry for about 1 minute until everything is well combined and the noodles have absorbed the sauce. Taste and adjust seasoning if needed, then serve immediately.