Wash, cut tops off of strawberries and slice them 1/4 inch thick then set aside. Line bottom of a 3-quart 13×9 baking dish with graham crackers and set aside. Combine cream cheese and sweetened condensed milk in a large bowl and beat with a mixer until smooth and creamy. Add pudding mixes and milk then continue mixing on low for 4-5 minutes or until mixture starts to thicken. Fold in 2 cups whipped topping until smooth. Pour half of the cream cheese mixture over graham crackers. Arrange a single layer of strawberry slices over cream cheese mixture. Top strawberries with another layer of graham crackers then cover with remaining cream cheese mixture. Top cream cheese mixture with another layer of strawberries.
Cover and refrigerate for 6-8 hours. When serving, top with remaining whipped topping. Crush remaining graham crackers and sprinkle crumbs over the top.