Place beef strips in slow cooker.
Combine oil, soy sauce, onion, garlic, sugar, salt and pepper, and ginger; pour over beef.
Cover and cook on LOW for 5 to 6 hours, or until meat is tender.
Add tomatoes and green peppers; cover and cook on LOW for 1 hour longer.
Combine the cold water and cornstarch to make a paste; stir into liquid in slow cooker and cook on high until thickened.
Serve over noodles or rice.