In a medium bowl, mix cream cheese and butter until smooth. Mix in powdered sugar and fold in whipped topping. Set aside.
In a separate bowl mix pudding, milk and vanilla. Fold this mixture in with the cream cheese mixture.
Spread half the mixture onto the first layer of Angel food cake. Add the top of the cake and add the rest of the mixture.
Refrigerate for at least one hour.
Right before serving, place chopped strawberries and whole strawberries on top.