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.
Rinse spaghetti with cold water to cool; drain.
Whisk soy sauce, teriyaki sauce, honey, and ground ginger together in a bowl.
Heat oil in a large skillet or wok over high heat. Cook and stir celery, carrots, sweet onion, and green onion in the hot oil until slightly tender, 5 to 7 minutes; add spaghetti and sauce mixture.
Continue to cook, tossing to mix, until the noodles and sauce are hot, about 5 minutes more.