Preheat oven to 175°C and grease and flour two 8-inch square cake pans.
Beat vegetable oil, 1/2 cup of sugar and egg yolks with electric beaters until fluffy.
Stir in lemon zest and vanilla. Stir in milk. Sift together pastry flour, baking powder and salt and gently stir into egg yolk mixture until blended.
Spread evenly into the 2 prepared pans. Whip egg whites with electric beaters until frothy, then gradually add the remaining 1/2 cup sugar and whip until whites hold a stiff peak.
Spread meringue evenly over batter in pans. Bake for 30 to 35 minutes, until a tester inserted in the center of the cake comes out clean. Cool cakes completely in the pan.
To assemble, turn one cake out onto a plate, meringue-side down. Top cake with half the strawberries and cream.
Place second cake layer on top, meringue-side up and top with remaining cream and fruit. Chill until ready to serve.