Bring a large pot of lightly salted water to a boil. Cook spaghetti in the boiling water until cooked through yet firm to the bite, about 12 minutes; drain.
Heat vegetable oil in a large skillet. Cook and stir celery and onion in hot oil until soft, 5 to 7 minutes. Pour white wine over the celery mixture; add ginger and garlic and toss to mix. Stir beet greens and stems, soy sauce, sesame oil, and fish sauce into the celery mixture; simmer together about 5 minutes. Add drained spaghetti to the skillet; toss to coat with the sauce. Cover the skillet and continue cooking until the beet greens are tender, about 5 minutes.