In a bowl, combine cracker crumbs, sugar and butter. Press into a greased 9-in. square baking dish. Bake at 350° 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 into prepared crust. Refrigerate for 4 hours or until firm.