In a bowl, combine cracker crumbs, sugar and butter. Press into a greased 9 inch square baking dish. Bake at 350 degrees for 10 minutes or until golden brown. Cool on a wire rack.
Combine strawberries and sugar in a small bowl; let stand for 20 minutes. In another bowl, dissolve gelatin in water. Drain berries, reserving the juice; add enough water to juice to measure 1 cup. Stir berries and juice mixture into gelatin. Refrigerate until partially set.
Meanwhile, combine marshmallows and milk in a saucepan. Cook and stir over low heat until blended and smooth. Cool to room temperature, about 15 minutes. Fold in whipped topping, then gelatin mixture. Pour mixture into prepared crust. Refrigerate dessert for 4 hours or until firm.