How to eliminate extra Drupal Logout Link
Try using the Devel Themer (https://drupal.org/project/devel_themer). That works kinda like a firebug/backtrace for themeing, and it should point you to where those links are coming from. Keep in mind Themer is a bit buggy, and can cause some issues, so you might want to switch it off when your done, but it should help you diagnose your problem.