Hi Will,
Office 365 for Business plans provide Exchange based email service. If you have an Exchange account and set up the account on Outlook for Mac and iPhone via Exchange, the calendar and contacts will be synced.
However, based on your description, I understand you don't have an Office 365 online account and you are using iCloud and other email accounts. Our forum focuses on Office 365 for Business Online services and they are not supported in this forum.
Thanks,
Xinyu