Hello,
If you use the Weblinks component for the links, they actually look like 'index.php?option=com_weblinks&catid=2&id=1&task=view' on Joomla's page and after you click it, it gets redirected to the external URL, so it is OK that JoomSEF makes nice link for this.
Try setting handling to nocache or skip for com_weblinks in JoomSEF's configuration to see if it helps.
Best regards,
ARTIO Support Team
Edit: My mistake, you cannot change the handling for weblinks component in current version. Try turning JoomSEF off to see if the links work and it is really JoomSEF's problem. If it is, try setting Error reporting to Maximum in Joomla Global configuration on the Server tab, so there will be actual error reported instead of blank page when you click the link.