In a large bowl, with a mixer on high speed (use whip attachment if available), beat eggs and sugar until thick and pale yellow, 5 to 6 minutes. In a small bowl, mix flour and baking powder. With mixer on medium speed, gradually add flour mixture in small increments and beat until smooth. Scrape batter into a buttered 9- by 13-inch baking pan.
Bake in a 325° regular or convection oven until a toothpick inserted in the center comes out clean, 30 to 40 minutes.
Meanwhile, in a blender, whirl condensed milk, evaporated milk, regular milk, Kahlua, and vanilla until well blended. Pour evenly over hot cake; let cool about 15 minutes, then cover and chill until cake has absorbed all the milk mixture, at least 3 hours, or up to 1 day.
Cut cake into squares or rectangles, lift out with a wide spatula, and set on plates. Top each piece of cake with a spoonful of whipped cream and garnish with strawberries.