Organizing and accessing contact information in Outlook.com
I've had similar problems recently and found the following worked for me. In my particular case I have used a personal, non-microsoft email address as the ID for my Microsoft Office 365 account for some time. Up until fairly recently I could add this as an Exchange ActiveSync account in both Outlook 2016 on my PCs/Laptops and on my HTC Android phone and get syncing of Contacts and Calendar between devices. I had to find out the ActiveSync Server name to do the configuration but it did work. (The only problems I encountered were Categories not syncing between WIndows devices and unable to create Contact Groups but these are known limitations of ActiveSync accounts).
A few weeks ago something changed that stopped this working. Not sure what it was but found that I could no longer configure the account in either Outlook 2016 or on my Android. After much trial and error I found the following resolved the problem. In my Office 365 account I created an alias using a newly created outlook.com address. I then made this the primary address for the account. I then used this address to configure an account in both Outlook 2016 and as an Outlook.com account on my HTC and all started working again. Also configured the account successfully on a friend's Samsung Galaxy S6. The new outlook.com address is still an ActiveSync account by I'm hoping (and have been assured by Microsoft Outlook.com support via a chat session) that this will be migrated to a Microsoft Exchange account in the coming months thus removing the limitations mentioned above.
Hope this helps.