Mix 3/4 tsp salt and 1/4 tsp pepper in bowl with cornstarch. Coat chicken pieces.
Heat 1 T oil in wok at medium high. Stir fry half of chicken 3 minutes and remove to a plate. Add another 1 T oil and stir fry rest of chicken with garlic, ginger, and white parts of onion 3 minutes. Add previously cooked chicken and vinegar and cook 30 seconds.
Add sesame oil, celery, red peppers, oyster sauce, hoisin sauce, tamari sauce, pepper and water, and cook, tossing, until chicken is cooked through, about 1 minute. Remove from heat.
Stir in green parts of onion and cashews. Serve over white rice.