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 15 by 10-inch baking pan.
Bake 350 degrees 35 to 45 minutes. Meanwhile, combine 3 milks, Kahlua, and vanilla in bowl. Pour milk mix over cake right out of oven. Let soak, refrigerated,
at least 3 hours. Serve with whipped cream and strawberries. Serves 12 to 16.