I want to change the style of the "category" links on the navigation on WP. Where do I find this file to edit it?
the category listing is normally in the sidebar but I believe you can place it anywhere. Check your stylesheet. It should be either using the standard class you have for sidebar boxes or a specific class for categories (it will be wrapped with its unique div if thats the case).
If you want to style your navigation using categories, (i assume you mean top horizontal navigation of your header) you can do that in your style.css file!