In a large bowl, toss the rutabaga and sweet potato with 2 tablespoons of the oil and season with salt and pepper. Spread evenly over a baking sheet (or divide it between two baking sheets if needed) and roast for 25 to 30 minutes, until tender.
Meanwhile, toss the pearl onions with the vinegar and 1/2 teaspoon of the remaining oil and season with salt and pepper. Spread the onions evenly over a baking sheet and roast for 12 to 15 minutes, until tender.
Put the remaining 1/2 tablespoon oil in a medium skillet over medium heat. Add the mushrooms and sauté until tender, 5 to 7 minutes, then add the kale and wilt it slightly, about 2 minutes. Remove all the vegetables from the pans into one large bowl, and set aside.