We used 6 (8-inch) disposable aluminum foil cake pans, so we could fill all the pans at once. This way, if you bake the layers in batches, the second batch is ready to go in the oven as soon as the first is done.
Preheat oven to 350°. Stir together first 3 ingredients and 1 cup sugar in a large bowl. Make a well in center of mixture; add oil, next 2 ingredients, and 1/4 cup water. Beat at medium-high speed with an electric mixer 3 to 4 minutes or until smooth.
Beat egg whites and cream of tartar at medium-high speed until soft peaks form. Gradually add remaining 1/4 cup sugar, 1 Tbsp. at a time, beating until stiff peaks form. Gently stir one-fourth of egg white mixture into flour mixture; gently fold in remaining egg white mixture. Spoon batter into 6 greased and floured 8-inch round cake pans.
Bake at 350° for 12 to 15 minutes or until a wooden pick inserted in center comes out clean. Cool in pans on wire racks 10 minutes; remove from pans to wire racks, and cool completely (about 1 hour).
Spread filling between cake layers, leaving a 1/4-inch border around edges (about 2/3 cup between each layer). Cover cake with plastic wrap, and chill 8 to 24 hours. Spread Strawberry Frosting on top and sides of cake. Chill 2 hours before serving.