In a medium bowl, combine the chicken pieces with soy sauce and cornstarch. Mix well and let it marinate for about 15 minutes.
Heat vegetable oil in a large skillet or wok over medium-high heat. Add the marinated chicken and cook until browned and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the sliced mushrooms, bell pepper, and onion. Stir-fry for about 3-4 minutes until the vegetables are tender.
Add the minced garlic and ginger to the skillet, cooking for an additional minute until fragrant.
Return the chicken to the skillet and add black pepper, oyster sauce, rice vinegar, and sugar. Stir well to combine and cook for another 2-3 minutes to heat through. Season with salt to taste.
Serve hot, garnished with chopped green onions over steamed rice or noodles.