Make the cake: Preheat oven to 325 degrees. Whisk together flour, 3/4 cup granulated sugar, the baking powder, and salt. Whisk together oil, egg yolks, and milk in a large bowl. Whisk flour mixture into egg-yolk mixture.
Beat egg whites with a mixer on high speed until frothy. Add cream of tartar and vanilla seeds or extract, and beat until soft peaks form. Gradually add remaining 3/4 cup granulated sugar, beating until stiff, glossy peaks form, about 5 minutes. Whisk one-third of the egg-white mixture into batter. Gently but thoroughly fold in remaining egg-white mixture with a rubber spatula.
Transfer batter to tube pan. Bake until top of cake springs back when touched, 52 to 55 minutes. Let cool upside down (over a bottle or on tube-pan feet) 1 hour.
Make the berries and cream: While cake is baking and cooling, combine strawberries, granulated sugar, lemon juice, and salt, and let sit, stirring occasionally, 1 hour. Just before assembling, beat cream and confectioners' sugar until medium peaks form.
Slide a paring knife around edges of tube and side of pan; release cake. Cut cake horizontally into 3 layers with a serrated knife. Transfer bottom layer to a cake plate or platter. Spread with half the berries, and drizzle with juices. Spread half the whipped cream over berries, then top with middle cake layer. Spread with remaining berries and whipped cream. Top with remaining cake layer. Refrigerate cake 1 hour. Sprinkle with confectioners' sugar, and serve with berries.