Preheat oven to 350F. Lightly grease a 9 x 5 loaf pan.
In a large bowl, mix together the sugar, eggs, oil, and vanilla. In a separate bowl, mix together the flour, baking powder and soda, and spices, and add the mixture to the wet ingredients in the bowl. Mix in the rolled oats, applesauce, and walnuts if using them.
Pour the mixture into the prepared pan. Bake the bread for 55 to 60 minutes until a toothpick inserted into the center comes out clean. Remove the bread from the oven and cool completely.
Store cooled bread, well wrapped, at room temperature for several days. This bread freezes well for longer storage.