In a medium bowl, combine oil, sugar, salt and baking soda. Add eggs, apples, nuts and vanilla. Pour mixture evenly into 3 round cake pans. Bake at 350 degrees for 25 to 30 minutes. Let cool on a wire rack.
Mix the flour and milk. Cook in a medium sauce pan until very thick. Let cool completely. Cream the butter and sugar using a mixer. SLOWLY Add the flour/milk mixture to the butter/sugar mixture. Add vanilla and beat into mixture until fluffy. Ice the cooled cake layers.