I'm having the exact same issue - Moved from Exchange to Exchange Online/365 and I can't remove the old account from Outlook for Mac 2011 (using Settings / Accounts / Delete). Outlook crashes every time.
Same if I go into Work Offline mode, unfortunately.
After some googling, I found this link to manually remove the account:
https://php.radford.edu/~knowledge/lore/article.php?id=400
- Shut down Outlook
- Delete the folder ~/Documents/Microsoft User Data/Office 2011 Identities/Main Identity and its subfolders.
This will remove everything from outlook, so if you have more than the 1 account set up, they will all be deleted. But it's a clean start.
Worked for me, as I only had the old Exchange account(s) so they all needed to be deleted anyway.
Then add the O365 account back, or even better, download the new version of Outlook for Mac (2015) and use it.
Hope this helps.