Can you figure out which classes are loading and from which stylesheet, using Firefox+Firebug? You need to figure that out if you want to see where the problem is.
In the above example there's actually two different carrousels, the first one is using Sponsors Carousel plugin, the other Shortcodes Ultimate, but both work the same way: overriding the plugin's CSS with the theme's CSS.
I don't know what else to say. It works that way.
A workaround is creating your custom plugin skin. Through FTP, locate the plugin's folder and duplicate the skin folder you wish to customize. Make the CSS changes in the original folder and leave the copied one intact, just in case. Be sure to comment your changes and make a backup copy of that folder.
Beware: with this workaround you'll loose any changes if the plugin gets updated. This is not good practice, I'm just posting so that you can get it to work.