Combine first 6 ingredients in a small saucepan over medium-high heat. Bring to a boil, and cook for 2 minutes. Combine cornstarch and water. Stir cornstarch mixture into soy sauce mixture. Bring to a boil; cook 1 minute.
Thread 2 shrimp, 2 scallops, 4 mushroom halves, and 3 green onion pieces alternately onto each of 8 (12-inch) skewers. Brush kebabs with oil, and place on a grill rack coated with cooking spray; cook for 3 minutes. Turn kebabs, and brush with half of soy sauce glaze; cook for 1 minute. Turn kebabs. Brush with remaining glaze; cook 1 minute or until seafood is done.