In a bowl, combine the first seven ingredients; add pork and toss to coat. In a nonstick skillet or wok, stir-fry carrots in 2 teaspoons oil for 2 minutes. Add zucchini and celery; stir-fry for 2 minutes. Add mushrooms; stir-fry for 2-3 minutes or until vegetables are crisp-tender. Remove and keep warm.
Stir-fry pork with marinade in batches in remaining oil for 2-3 minutes or until meat is no longer pink. Return the vegetable mixture and all of the pork to the pan. Add spinach; stir-fry for 1-2 minutes or until spinach is tender.