Preheat your oven to 350°F (175°C). Grease and flour a 9x13-inch baking pan.
In a large mixing bowl, combine the flour, sugar, baking powder, and salt. Mix well.
Add the whole milk, vegetable oil, eggs, and vanilla extract to the dry ingredients. Beat with an electric mixer on medium speed for about 2 minutes until smooth.
Pour the batter into the prepared baking pan and spread it evenly. Bake for 30-35 minutes, or until a toothpick inserted in the center comes out clean.
Allow the cake to cool in the pan for about 10 minutes. Then, using the handle of a wooden spoon, poke holes all over the cake.
In a separate bowl, whisk together the instant pudding mix and cold milk until smooth. Pour the pudding over the cake, making sure it fills the holes.
Cover the cake with plastic wrap and refrigerate for at least 2 hours, or overnight for best results.
Once chilled, spread the whipped topping over the cake. Decorate with sliced bananas and crushed vanilla wafers on top.
Serve immediately or keep refrigerated until ready to serve.