Cream together cream cheese and white sugar in a bowl until smooth. Stir in sour cream, almond extract, and 1/2 teaspoon vanilla extract.
Fold remaining 1 teaspoon vanilla extract and confectioners’ sugar into thawed whipped topping in a separate bowl until thoroughly combined.
Gently fold the whipped topping mixture into the cream cheese mixture until combined.
Layer the bottom of a glass serving bowl with 1/4 angel food cake pieces. Top with 1/4 cream mixture and a layer of strawberries; continue layering three more times until all the cake and cream mixture is used. Finish with a layer of strawberries. Chill until ready to serve.