Combine all cake ingredients in a mixing bowl. Beat at medium speed for 2 minutes.
Pour batter into a greased 9x13" cake pan.
Bake cake in a preheated oven at 350° for 30-35 minutes or till a toothpick inserted in the middle comes out clean.
Cool the cake completely, then use a round spoon handle to poke holes all over the cake about an inch apart.
Combine pudding mix and milk and whisk for 2 minutes. Quickly pour over the cake. Get as much pudding into the holes as you can. Cover cake and chill for at least 30 minutes.
Place vanilla wafers in a bag and crush them with a rolling pin. Set aside.
Whip cream till soft peaks form. Add powdered sugar and vanilla and beat till well mixed.
To serve, cut the cake into slices. Top with sliced bananas, whipped cream, and crushed vanilla wafers. Refrigerate any leftovers.