Heat oven to 250 degrees F. Cover 2 baking sheets with foil.
Combine egg whites and cream of tartar in large bowl. With electric mixer on medium speed, beat whites to soft peaks. Gradually add sugar a few tablespoons at a time, beating constantly, until fully incorporated, 7 to 10 minutes; meringue should form glossy, stiff peaks, without grainy sugar granules.
Transfer meringue to large pastry bag fitted with 1/4-inch round tip. Pipe sixteen 2-1/2-inch square box outlines and eight 2-1/2-inch circles onto prepared baking sheets. Fill in outlines with a small amount of meringue, spreading with spatula. Build walls on top of base at the edges for 8 of the squares and for the 8 circles, using a continuous stream of meringue. Do not pipe higher than 1-1/4 inches, as walls may fall over.
On the 8 square tops without walls, pipe a dollop for the handle. Once completed, there should be 8 square boxes with 8 lids and 8 round boxes without lids.
Bake in 250 degree F oven for 50 minutes; the meringues should be firm without turning brown. Remove the baking sheets to wire racks to cool. Once the meringues are cooled, gently peel the boxes and tops from the foil-lined baking sheets. If meringues are sticking, cut around the meringues and remove from the baking sheet, with the foil attached to the meringue. Then slowly and carefully peel the foil from the bottom of the meringue. To prepare ahead, bake, cool and store meringues in airtight container at room temperature for a day or two.
Toss together strawberries, blueberries, blackberries, raspberries, sugar and orange juice in large bowl until well mixed.
Place 2 boxes on a dessert plate. Fill each with 1/4 cup of the mixed berry mixture. Top the square box with its lid, or prop the lid on one side. Serve at once. Makes 8 servings.