Beat egg whites until very stiff; add 1/3 c. sugar to make a stiff meringue. Set aside. In a large bowl, sift together the flour, baking powder, baking soda, & salt. Make a well in the center of the dry ingredients and add the oil, bananas, 1/3 c. milk & vanilla; beat 1 min. Add 1/3 c. milk and egg yolks; beat 1 min. Fold in meringue and nuts. Pour into 2, 9" round, layer pans that have been well greased and floured. (May use a 9x13 pan) Bake at 350~ for 30-35 minutes for layers, 40-45 minutes for rectangle pan. Remove from oven, cool in pans for 5 minutes, then turn out onto a rack to finish cooling. When cool, split layers into 2 each so you have a total of 4 layers of cake. Place 1st layer on serving platter and proceed with assembly.Directions continued part 2.