Cook noodles until al dente. Drain. Rinse under cold water. Toss with 1 teaspoon oil. Set aside.
Whisk soy sauce, oyster sauce, rice vinegar, sesame oil, sugar, red pepper flakes, and water. Set aside.
Shred cabbage, julienne carrot, slice bell pepper. Mince garlic and ginger. Slice green onions, separating whites and greens.
Heat 1 tablespoon oil in wok over high heat.
Add cabbage, carrot, and bell pepper. Stir-fry 3 to 4 minutes until tender-crisp.
Transfer vegetables to plate.
Add remaining 1 tablespoon oil to wok.
Add garlic, ginger, and white parts of green onions. Stir-fry 30 seconds.
Add noodles. Toss to coat with aromatics.
Return vegetables to wok. Add sauce.
Toss together over high heat 2 to 3 minutes until evenly coated and heated through.
Taste. Adjust seasoning if needed.
Remove from heat. Stir in green parts of green onions.
Transfer to bowls. Garnish with sesame seeds, green onions, and lime wedges.
Serve hot immediately.