Preheat oven to 325°. In a large bowl, combine the cake mix, eggs, applesauce and oranges. Beat on low speed for 30 seconds; beat on medium for 2 minutes.
Pour into two greased and floured 9-in. round baking pans. Bake until a toothpick inserted in the center comes out clean, 30 minutes. Cool in pans for 10 minutes before removing to wire racks to cool completely.
In another bowl, beat whipped topping, pineapple and pudding mix. Spread between layers and over top and sides of cake. Chill.