To make the cake: Preheat the oven to 350 degrees F. Lightly grease and flour a 9 by 13-inch baking dish and set aside.
In the bowl of a mixer, beat the egg whites on low speed until soft peaks form. Add the sugar gradually with the mixer running and peak to stiff peaks. Add the egg yolks 1 at a time, beating well after the addition of each.
Sift together the flour and baking powder and add to the egg mixture, alternating with the milk. (Do this quickly so the batter does not lose volume.) Add the vanilla. Bake until golden, 25 minutes.
Sauce
In a mixing bowl, combine the sweetened condensed milk, evaporated milk, milk, and vanilla. Allow the cake to cool slightly. Using a fork, or two, poke wholes all over the cake so that it will better absorb the vanilla sauce. Slowly pour the vanilla sauce over the cake. Cover and chill at least four hours. Serve with whipped cream and strawberries.