Step 1: Prepare the Cheesecake Layer: In a large bowl, beat softened cream cheese and powdered sugar until smooth. Stir in vanilla extract. Gently fold in half of the thawed whipped topping until no streaks remain. Set aside.
Step 2: Prepare the Vanilla Pudding: In another large bowl, whisk together instant vanilla pudding mix and cold milk for 2-3 minutes, until thickened. Let stand for 5 minutes.
Step 3: Assemble the Layers: In a large (9x13 inch) clear dish, spread a thin layer of vanilla pudding on the bottom. Arrange a single layer of vanilla wafers over the pudding. Top with a layer of sliced bananas.
Step 4: Add Cheesecake and Strawberries: Spread half of the cream cheese mixture over the bananas. Add a layer of sliced strawberries.
Step 5: Repeat Layers: Top the strawberries with another layer of vanilla wafers. Follow with the remaining vanilla pudding, then another layer of sliced bananas. Spread the remaining cream cheese mixture over the bananas.
Step 6: Final Topping: Top with a final layer of vanilla wafers, then the remaining half of the whipped topping. Arrange any remaining sliced strawberries and a few vanilla wafers on top for garnish.
Step 7: Chill: Cover the dish tightly with plastic wrap and refrigerate for at least 4 hours, or preferably overnight, to allow the wafers to soften and flavors to meld. Serve chilled.