Crush about 3/4 of the Oreos into fine crumbs. Set aside. Chop remaining cookies for topping.
In a bowl, beat cream cheese, butter, and powdered sugar until smooth and fluffy.
In another bowl, whisk milk and pudding mix until thickened (about 2 minutes), then let sit 5 minutes.
Fold whipped topping into the cream cheese mixture until smooth.
Gently fold in the prepared pudding mixture until fully combined.
In a 9×13 dish, layer 1/3 of Oreo crumbs on the bottom.
Add half of the pudding mixture.
Repeat layers: Oreo crumbs, remaining pudding, then finish with remaining crumbs on top.
Cover and refrigerate at least 2 hours (or overnight).
Before serving, top with chopped Oreos and gummy worms.