Wash the rhubarb, trim off the ends of the stalks, then slice them crosswise into 1/2-inch chunks. If the stalks are very thick, halve them lengthwise first. Toss with the sugar, tapioca, orange juice, zest, and cloves.
Arrange the mixture in an 8-by-10-inch gratin dish and let stand while you preheat the oven to 400°F (220°C). Cover the dish with foil and bake until the fruit is tender when pierced with a knife, 35 to 45 minutes.
Meanwhile, if you're using strawberries, rinse them quickly, then slice thickly. Plunge mulberries briefly into water and remove any stems. When the rhubarb is done, remove it from the oven, scatter the berries over the top, and let stand with a piece of foil placed loosely over the top. The heat of the rhubarb will open the flavor of the berries, cooking them slightly. Serve the dessert chilled or at room temperature, garnished with cream and crème fraîche whipped together until billowy, and the candied ginger.