Preheat your oven to 350°F. Crush Oreo cookies into fine crumbs and reserve 1/2 cup for later. Mix crushed Oreos with melted butter and press into the bottom of a 9x13-inch baking dish.
Beat softened cream cheese until smooth, then add powdered sugar and vanilla extract. Fold in 1 cup of whipped topping and spread over the Oreo crust.
Whisk together chocolate pudding mix and 2 cups of milk for about 2 minutes until thickened. Pour over the cream cheese layer. Repeat with vanilla pudding mix and pour over the chocolate layer.
Top with remaining whipped topping, drizzle chocolate syrup, and sprinkle reserved crushed Oreos. Cover and refrigerate for at least 4 hours or overnight.
Notes
Allow the lasagna to chill for at least 4 hours for best results.