Why arn't changes I am making in CSS appearing? This is weird. I've just started at a company that uses Drupal (I havent used it before) and I've been tasked with making some simple CSS changes to a site.

I find the site's theme folder and corresponding CSS and make a simple change just to test things out. Nothing happens. I clear the cache via admin and get a 500 error. Fine. So I use drush to clear CSS and JS. It says it works but still no change. I clear my browser cache too just to be sure. 

I use Chrome's inspector to trace back the paths of the CSS files I'm working on - they're correct. I even check the themes .info file to see if all the .css files are linked - they are.

So...what am I missing here? What on Earth is going on?

(Edit: CSS aggregators are off)
I'd turn off CSS aggregation temporarily to see if that makes any difference. The settings are in admin/config/development/performance

That way you can see which CSS files are being used directly. This sounds like it might be a configuration problem with the server itself and not something with Drupal.

Also, check the response headers for the CSS. That will give you more info about whether it's serving cached versions and if there's something like a reverse proxy serving old versions of the files.