Preheat oven to 350 degrees F (175 degrees C). Grease and flour 2 - 9 inch cake pans.
Sift together the flour, sugar, baking soda and salt. Set aside.
In a large bowl, combine the oil, eggs, pineapple, bananas and nuts. Add flour mixture, and mix together by hand.
Pour batter into prepared pans and bake for 1 hour or until a toothpick inserted in center comes out clean. Remove from oven and allow to cool on racks.
Prepare the frosting by blending together the cream cheese, butter, sugar and vanilla until smooth. Evenly spread frosting on middle, sides and top of cake.