Combine chicken strips, cornstarch, soy sauce, ginger, and garlic powder in a large resealable plastic bag. Coat chicken with marinade, squeeze out excess air, and seal bag. Refrigerate for 1 to 1 1/2 hours.
Bring a large pot of lightly salted water to a boil. Cook spaghetti in the boiling water, stirring occasionally until cooked through but firm to the bite, about 12 minutes. Drain.
Heat 3 tablespoons vegetable oil in a large skillet over medium heat. Remove chicken from marinade and shake off excess; cook and stir in hot oil until chicken is no longer pink in the center, about 5 minutes. Stir in onion, celery, carrots, and broccoli. Add 1 tablespoon vegetable oil, if needed. Cover and cook until vegetables are tender, stirring occasionally, about 5 minutes.
Stir spaghetti into chicken and vegetable mixture; cover and simmer for 5 minutes more.