Synchronise Office 365 Outlook Calendar and Tasks with Nexus 5

I fruitlessly posted the following question in another thread (http://answers.microsoft.com/en-us/office/forum/office_365hp-outlook/synchronise-office-365-outlook-calendar-and-tasks/d7efc108-648c-47d9-a4b5-58c33f9683c8?msgId=9c46ce3f-1a1c-4f4b-9a25-5cf41181e38d ) and was directed here because the tech thought the issue related to Mac Office 2011 rather than the "Office/Office 365 Home Premium/University/Microsoft Office Outlook/Office on Android" thread (go figure).  I am looking for a solution, not another referral.

Is it possible to synch 365 calendar and tasks with a Nexus 5?

If so, how?

In response to a request for more specific information I added the following ...

I moved from Office 2011 Home and Student to Office 365 for two reasons

• I dislike Apple ICal and iMail and I wanted Outlook Mail, Calendar and Tasks
  
• I need to sync Outlook Calendar and Tasks with my phone
• The discussion forums I had read led me to believe that only Office 365 would allow this
  

I am a one person business and a student, with a range of email accounts for business, personal use and one for my university.

MacBook Pro

• I am running Office 365 on my MacBook Pro (Mac OS X 10.7.5).
• All my Outlook email accounts were set up on my Mac as IMAP except for my university email account which was set up as an Exchange Account. 
• I tried but could not set up an Exchange Account for my
  

Nexus 5

• My Phone is a Nexus 5 with the latest Android
• I have loaded Office Mobile App (Only seems to support Word and Excel)
• I also have Lync 2013 (but I don't have any idea whether it is of any use to me.

Finally:

• since I posted my initial question, I have loaded a free phone App called SyncMate which has allowed me to manually sync my Mac's Outlook Calendar with my phone. 
  
• I am still unable to sync tasks to my phone.
• SyncMate is not an adequate solution.

The marketing material regarding Office 365 specifically states

• Outlook is now automatically connected to your Microsoft web mail account. Sync tasks and calendars with Outlook to put all your plans together.

( http://office.microsoft.com/en-au/university/ )

I need to sync my phone with my Mac (not my university). 

• Perhaps I need to establish a private "Microsoft web mail account"
• If so, how??
  

Please advise a solution urgently!!

Regards

Steve