A user-defined style that you edit/create in EG's Style Manager is just a css stylesheet.
Here is how you can use an existing css stylesheet in ODS statements:
https://support.sas.com/rnd/base/ods/templateFAQ/Template_csstyle.html#existing
So, find the physical location of your .css file (URL field in EG's Style Manager), then copy the .css file to a location on your webserver that your html pages can reference.
And more doc on css stylesheets with ODS:
https://support.sas.com/rnd/base/ods/templateFAQ/Template_csstyle.html
Casey