Blend softened cream cheese with a mixer until smooth, then add softened butter and mix until combined. Gradually add powdered sugar and thawed whipped topping, mixing on low speed until fully incorporated; set aside.
Prepare the pudding with milk according to package instructions in a large bowl. Fold in the cream cheese mixture with a spatula and set aside.
Crush Oreo cookies (including filling) in a food processor until fine. You may need to work in batches.
Press half of the crushed Oreos firmly into the bottom of a 9x13-inch pan to form the crust.
Spread the pudding mixture evenly over the Oreo crust.
Top with remaining Oreo crumbs, then refrigerate for at least 2 hours or overnight to set.
Melt white candy melts, coat Nutter Butter cookies, and let dry. Melt chocolate chips, pipe "RIP" onto cookies, and allow them to dry for tombstones.
Once set, decorate the cake with Nutter Butter tombstones, gummy worms, and any other spooky candies. Serve chilled.