Preheat the oven to 350 degrees F (175 degrees C). Grease and flour a 9x13-inch baking dish.

Make cake: Prepare cake mix as directed on the package, using 1 1/3 cups water, 3 eggs, and 1/3 cup oil. Pour batter into the prepared dish.

Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 30 minutes. Allow cake to cool on a wire rack.

Poke holes on top of cooled cake using a fork. Purée thawed strawberries with juice in a blender or food processor until smooth. Spoon over top of cake.

Make topping: Prepare pudding mix as directed on the package, using 1 cup milk. Fold whipped topping into pudding until combined, then spread over cake. Arrange strawberries on top.

Refrigerate cake for at least 4 hours before serving.