Preheat the oven to 400 degrees F.
Cut off the top 1/3 of each orange. Use a curved grapefruit knife to scoop out the insides of the oranges. Reserve the pulp for a fruit salad or other use. Reserve the orange shell to use as a cooking vessel.
Bring a medium skillet of salted water to a simmer. Add the scallions and cook for 30 seconds. With tongs, rinse the scallions under cold running water; pat dry on paper towels.
Holding the root ends, run the back of a large knife down the length of the scallions, pressing down to squeeze out as much liquid as possible. Slice into 1-inch pieces. In the same skillet, slip the oysters, squid, and shrimp into the water and poach over low heat until the edges of the oysters curl, 10 to 15 seconds. Immediately transfer to a bowl; do not overcook.
Pour 2 tablespoons of the White Miso Sauce into each orange shell. Spoon the seafood mixture in next, mounding as needed. Finally, top with another 2 tablespoons of the White Miso Sauce.
Bake the seafood-stuffed oranges for 10 minutes, or until hot throughout. Transfer to individual plates and serve immediately.