In a small bowl, whisk together soy sauce, oyster sauce, cornstarch, and water until smooth. Set aside.
Heat vegetable oil in a large skillet or wok over medium-high heat.
Add the chicken strips to the skillet and cook for 5-6 minutes, stirring frequently, until the chicken is cooked through and lightly browned. Remove chicken from skillet and set aside.
In the same skillet, add garlic and ginger and sauté for 30 seconds until fragrant.
Add red bell pepper, broccoli, carrot, snap peas, and mushrooms to the skillet. Stir fry for 5-7 minutes until vegetables are tender-crisp.
Return the cooked chicken to the skillet with the vegetables.
Pour the sauce mixture over the chicken and vegetables. Stir well and cook for another 2-3 minutes until the sauce thickens and coats everything evenly.
Drizzle sesame oil over the stir fry and toss to combine.
Remove from heat and garnish with sliced green onions and toasted sesame seeds.
Serve immediately with steamed rice or noodles if desired.