Position a rack in the center of the oven and heat the oven to 425ºF. Line a rimmed baking sheet with foil, creating a crosswise ridge, separating the sheet into two compartments.
Remove the stems and leaves from the beets and reserve. Put the beets on one side of the divided foil-lined baking sheet and the fennel on the other. Drizzle the vegetables with 1/4 cup of the oil divided between them, 1/2 teaspoon salt, and 1/2 teaspoon pepper. Position the fennel cut side down on the baking sheet. Cover the baking sheet with foil and roast until the vegetables are tender when pierced with a paring knife, about 45 minutes for the fennel and 1 hour for the beets. Remove the vegetables from the oven as they become tender and set aside. When the beets are cool to the touch, remove the skins, quarter, and slice into 1/2-inch wedges. Remove the tough outer layer of the fennel, and slice the remainder of the bulb lengthwise into 1/4-inch slices.
Meanwhile, bring a 6-quart pot of well-salted water to a boil. Have an ice bath ready. Wash the beet greens thoroughly and separate the stems from the leaves. Slice the leaves into thin ribbons, and the stems into a small dice. Blanch the greens and stems separately until just tender, about 2 minutes each. Transfer the greens to the ice bath with a slotted spoon. Strain the stems into a mesh strainer. When the greens are cool to the touch, squeeze out as much water as possible and coarsely chop.
Slice off the ends of the oranges to expose the fruit. Stand the fruit on a cut end, and slice off the skin and pith, following the natural curve of the fruit from top to bottom. Working over a bowl to collect the juice, cut on each side of each membrane to free the segments and transfer to a small plate. Squeeze the membranes and the skin over the bowl to extract more juice.
In a small bowl, whisk together 3 tablespoons of the reserved orange juice, 2 tablespoons of the remaining olive oil, and the balsamic vinegar. Season to taste with salt and pepper. Transfer the beet wedges, greens, and stems to a medium bowl, and the fennel slices to small bowl. Divide the dressing between the bowls, season with salt and pepper to taste, and toss until well coated.
Transfer the beets to a large serving platter or plates, top with the fennel, beet stems, orange slices, and walnuts, and serve.