Grease and flour 2 layer pans 8 or 9 x 1 1/2. Beat egg whites until frothy. Gradually beat in 1/3 cup sugar, beating until very stiff and glossy. Set aside.
Blend flour, sugar, baking powder, salt and soda in another bowl. Add oil, bananas, half of buttermilk and flavoring. Beat 1 minute medium speed. Scrape sides and bottom of bowl constantly.
Add remaining buttermilk and egg yolks. Beat 1 minute more by mixer scraping bowl frequently. Fold in the meringue. Fold in nuts gently. Pour into pans. 8 inch 30 to 35 minutes; 9 inch 25 to 30 minutes; oblong pan 40 to 45 minutes.
Preheat oven 350 degrees.