Preheat oven to 400 degrees F (200 degrees C). Combine pudding mix and cold milk; fold in whipped topping. Refrigerate until ready to use.
Unfold pastry on a cool, lightly floured surface. Cut into 3 strips along fold marks, then cut each strip into four equal pieces. Place 2 inches apart on a baking sheet.
Bake for 15 minutes in the preheated oven, or until golden brown. Remove from baking sheet, and cool.
Split pastries into 2 layers, setting the 8 best looking tops aside. Spread 8 bottom layers with dollops of the pudding mixture. Top each with a layer of strawberries, a small amount of pudding, and another pastry layer. (A small amount of the pudding mix on top of the berries will help keep the layers together.) Spread with remaining pudding mixture and strawberries, and top with remaining pastry layers (the best looking ones). Sprinkle with confectioner's sugar.
