Preheat the oven to 350°F, spray your cake pans (two 4 inch and two 6 inch) with Baker's Joy, and line with parchment rounds. Wrap with wet baking strips, if using. Set aside.
In a medium bowl, sift together the flour, baking powder, and salt. Set aside. In a measuring glass, combine the milk, oil, and vanilla. Set aside.
Beat the butter and sugar on a medium speed until light and fluffy, about 5 minutes, scraping the bowl down as needed.
Add the egg whites two at a time, more or less, mixing until combined after each addition. Scrape down the bowl as needed.
Add 1/3 of the dry ingredients to the mixer and beat on low until just combined. Add half of the liquids and beat until just combined. Repeat with another third of the dry ingredients, the remainder of the liquids, and finally the remainder of the dry, beating until almost combined. Scrape down the bowl as needed.
Gently fold in the crushed Oreos. Be careful not to over mix the batter, but you do want the cookie pieces evenly distributed.
Fill the 4 inch pans with 6 oz of batter and the 6 inch pans with 14 oz of batter. Bake the 4 inch pans for 30- 33 minutes and the 6 inch pans for 35- 38 minutes. The cakes should be golden brown, spring back when touched, and a skewer should come out clean.
Cool cakes in their pans for 10 minutes before transferring to a cooling rack. Cool completely before frosting.