Microsoft Outlook for Mac 2011 "Not Responding" after upgrade to Mac OS X 10.11 El Capitan
Microsoft has an update to fix the problem now.

For more information, check out this knowledge base article documenting the problem: https://support.microsoft.com/en-us/kb/3098396


  Shortly after you start Microsoft Outlook for Mac 2011 on Mac OS X El Capitan (version 10.11), Outlook hangs when it tries to sync with the server. The Spinning Wait cursor is displayed, and the application status is displayed as "Not Responding."
  
  [...]
  
  This issue occurs in Outlook for Mac 2011 version 14.5.5 and earlier versions when they are running on Mac OS X El Capitan (version 10.11).


To install the fix, you can either:


Open Outlook and click Check for Updates on the help menu (if your outlook freezes before you can update, you can create a blank profile temporarily by ALT-Clicking on the Outlook icon),
Download the update package at: https://www.microsoft.com/en-us/download/details.aspx?id=49183