The ‘default’ theme that you are using is built using a php file that converts to CSS at run time. Looking at your site as a guest I can see that it has not been built and is therefore missing most of the rules. However – why it should successfully build when logged in and not otherwise is a mystery and is going to be environmental in some way.
One thing you could try would be to turn on the compression and CSS cache (options > global) and them IMMEDIATELY run your forum. If that looks OK see if it holds for non-logged in users. But there is an underlying reasons why things are happening and it would be much better to resolve those. Something is stopping the php being executed…
You also have a javascript issue with your site which WILL effect the forum and possibly other plugins as well. Your WP theme is riding roughshod over the WP API and loading a second, older and non-standard copy of the jQuery library and this is triggering errors. This is explained here:
http://codex.simple-press.com/codex/faq/troubleshooting/what-is-this-jquery-conflict/