Combine mushrooms and 2 cups boiling water; cover and let stand 30 minutes or until soft. Drain mushrooms, and cut into 1/4-inch-wide strips; set aside.
Cut squid into 1/4-inch-thick rings; set aside.
Bring 1/2 cup water to a boil in a large Dutch oven. Add clams; cover and cook 3 minutes or until shells open. Discard any unopened shells. Remove clams with a slotted spoon; set aside. Pour cooking liquid into a bowl; set aside.
Heat oil in pan over medium-high heat. Add garlic, and sauté 2 minutes or until golden. Add reserved cooking liquid, daikon radish, shrimp, and broth. Bring to a boil; cook 2 minutes. Add fish balls; cook 1 minute. Add mushrooms, squid, clams, cabbage, and remaining ingredients; cook an additional minute.
Note: This soup is great the day it is made but will keep for up to one week in an airtight container in the refrigerator. Reheat slowly over low heat.