How to use my style.css file outside of wordpress subdomain?

If you’re using an absolute reference like that, you’d want to include the full file path, like http://diginomics.com/wp-content/themes/THEMENAME/css/style.css

I believe any time you call the functions like get_stylesheet_directory() or get_stylesheet_directory_uri() it will return the path for the current theme.

Just keep in mind that all themes need a style.css file.

I would have posted this in a comment but I’m not allowed yet.