Hi Bill_H,
How did you set up your Office 365 account on Outlook application, POP/IMAP, automatically set-up or manually set-up?
I would like to suggest you refer to the following article to set up your account automatically.
To Set up Outlook for Mac 2011: http://help.outlook.com/en-us/140/gg471164.aspx
In addition you may try the steps to troubleshoot this issue for Outlook 2010:
• Use Exchange online mode to instead of Cache mode.
How to turn on or off Cached Exchange Mode: http://support.microsoft.com/kb/829918
• Create a new profile to check if it works.
How to create and configure email profiles in Outlook: http://office.microsoft.com/en-us/outlook-help/turn-on-or-off-cached-exchange-mode-HP010355560.aspx
After doing all that please check whether it is calendar synchronize with Outlook.
Thanks,
Shyamal