If using dried noodles, soak in room temperature water for 30 minutes until pliable. Fresh noodles just need rinsing. Mix oyster sauce, soy sauces, sugar, and fish sauce in a bowl.
Heat wok or large skillet over high heat until smoking. Add 2 tablespoons oil and sear chicken for 90 seconds per side until just cooked. Remove to a plate.
Add remaining oil to wok. Stir-fry garlic and chilies for 15 seconds until fragrant. Add onion and bell pepper, cooking for 1 minute.
Add drained noodles, sauce mixture, and water to wok. Toss vigorously to coat noodles. Let sit 30 seconds to char slightly, then toss again.
Return chicken and green onions to wok and toss. Remove from heat and immediately add Thai basil, tossing until just wilted.
Serve immediately while hot with lime wedges on the side.