Put a rimmed baking sheet in the oven and preheat to 400 degrees F. Toast the wheat berries in a large dry pot or Dutch oven over medium-high heat, stirring often, 6 to 7 minutes. Add 8 cups water and season with salt. Bring to a boil, then reduce the heat to a gentle simmer and cook, stirring and scraping the bottom of the pot occasionally, until the wheat berries are tender but still slightly chewy, 1 hour to 1 hour 10 minutes, adding up to 1 cup more water if needed. Drain. Wipe out the pot and reserve.
Meanwhile, place the beets on a large sheet of foil; drizzle with 1 tablespoon olive oil and season with salt and pepper. Fold and crimp the edges to form a packet, leaving room for steam to circulate. Transfer the packet directly to the oven rack and roast until the beets are tender when pierced with a knife, 40 to 45 minutes. Let cool slightly, then rub off the skins with a paper towel and cut into wedges.
Meanwhile, remove the hot baking sheet from the oven and drizzle with 1 tablespoon olive oil. Add the carrots and season with 1/4 teaspoon salt and a few grinds of pepper; toss. Roast until tender, 20 to 25 minutes.
Heat 2 tablespoons olive oil in the reserved pot over medium-high heat. Add the red onion, fennel, garlic, ginger, 1/2 teaspoon salt and a few grinds of pepper; cook, stirring occasionally, until the onion is soft and the fennel is crisp-tender, about 6 minutes. Add the wheat berries, carrots and remaining 1 tablespoon olive oil. Cook, stirring, until warmed through, 2 to 3 minutes. Add the orange juice, lemon juice and all but 2 tablespoons parsley; season with salt and pepper. Stir in the beets. Sprinkle with the remaining parsley. Serve warm or at room temperature.