I don't know if it is related, but I think there is a problem with the Piwik Integration. Some page loads take almost 20 seconds while it is enabled. When it is disabled, loading times are normal (about 0.5 seconds). Try navigating the wiki while the Piwik Integration is disabled (I just disabled it now).
I looked at the code and every forum page load is waiting for a response from your piwik installation over HTTP before it serves the forum page. There are 2 problems with this: if you are accessing an external URL over HTTP via PHP, you should use some code where you can set a timeout -- like curl with a 3 second timeout, not file_get_contents(url) which seems to have no timeout. Further, if the piwik installation is on the same server, it makes no sense to access the API over HTTP. You should just read/include the files directly. Finally, if the piwik API absolutely must run over HTTP (and I don't see why it must), it seems it is just returning a Javascript resource. For an integration, you should be able to either fetch the resource once and cache it, or know the Javascript format and generate from within the integration. If you must go through the API (I don't see why you must for a local piwik install), you may as well just do this on the front-end (use Javascript to load the remote Javascript as if it was text, then execute it as Javascript). jQuery, which is bundled with XenForo, has this capability.