Preheat oven to 325 degrees F (165 degrees C). Grease and flour two 8x4 inch bread loaf pans.
In a large bowl, beat eggs until light yellow and frothy. Add oil, brown sugar, white sugar, grated zucchini, bananas, and vanilla; blend together until well combined. Stir in the flour, cinnamon, baking powder, baking soda, and salt. Mix in the cranberries and nuts. Divide the batter evenly between the two prepared loaf pans.
Bake in the preheated oven until a toothpick inserted in the center comes out clean, about 50 minutes. Allow to cool in the loaf pans on a wire rack before removing and serving.