Are you specifically interested in graphical output or, as implied by your subject, in tabular output created by PROC REPORT??
The easiest way to find out how a SAS style template (like MEADOW or SEASIDE) will translate to CSS style property/value format is to use ODS to create a CSS file for you. You can do this on a one-time basis, by using ODS HTML and the STYLESHEET= option to make a CSS file like this:
ods html path='c:\temp' (url=none)
proc print data=sashelp.class(obs=1);
ods html close;
If you use the above code, then the c:\temp directory will hold a file called "copy_of_meadow.css" that you can open with Notepad and edit.
Alternately, if you have SAS Enterprise Guide, there is a very nice Style Wizard that will allow you to make a new CSS file using MEADOW as your starting point (or the style of your choosing). This Style Wizard is actually a CSS editor because EG uses a CSS version of the SAS style templates with the reports created by EG.
You might want to open a track with Tech Support on this question, as the use of CSS files with a stored process is usually done with an override to the automatic variable &_ODSSTYLESHEET (same concept as &_ODSDEST).
However, not all client applications will receive HTML results and some client applications (such as Web Report Studio) require that the CSS be defined in a special XML file that is available on the Middle Tier configuration files.
In addition, it is not entirely clear where you expect your &_ODSDEST of TAGSETS.NOSTYLE to be used. In fact, there already is a "nostyle" destination -- well, there are 2 -- ODS PHTML and ODS CHTML -- either of those might work for you instead of trying to come up with your own TAGSET template based on TAGSETS.HTML4. It is possible that a simple override of:
%let _ODSDEST = CHTML;
might work for you without using a STYLESHEET at all.
I suspect you have some log messages about STYLE not found or TAGSET not found and that means that there is a certain amount of debugging required that will mean that someone has to look at ALL your code and understand your particular method of invoking this stored process.