Make vanilla pudding. Simmer 1 ½ cups milk with sugar and a pinch of salt over low heat just until warm. Whisk egg yolks with remaining ½ cup milk and cornstarch in a medium bowl. Slowly add milk to egg mixture, whisking constantly. Pour the pudding back into the pot and bring to a simmer over low heat, whisking constantly until thickened. Remove from heat and transfer to a bowl. Cover with plastic wrap directly touching the surface and let cool.
Make strawberry pudding. Follow the same steps as the vanilla pudding but heat milk with sugar, pinch of salt, and strawberry puree. Continue same steps for the eggs and finishing the pudding.
Make chocolate pudding. Follow the same steps as the vanilla pudding but heat milk with sugar, pinch of salt, and cocoa powder. Continue same steps for the eggs and finishing the pudding.
Assemble pudding. Spread chocolate pudding in bottom of a 8x8 baking dish or in individual serving cups. Top chocolate pudding with wafers and banana slices. Spoon strawberry pudding on top followed by more wafers and banana slices. Finish with vanilla pudding and a final layer of wafers. Transfer pudding to the fridge and chill for at least 4 hours or overnight.
Whip heavy cream with powdered sugar until stiff peaks form. Top neopolitan banana pudding with whipped cream and garnish with fresh strawberries and crushed wafers if desired.