You won't sync phone <==> phone <==> desktop, you'll sync devices <==> server <==> desktop -so you need something to sync to the server.
The easiest is using an outlook.com account (or Office 365 or Exchange).
Does the android sync icloud calendar and contacts? (I will need to charge my android and check) if so, you could sync to icloud, using the icloud addin in outlook. That could be the second best and free - but the icloud is a separate data file in Outlook, which many people don't like.
Another option is using
companionlink or gsyncit to sync outlook desktop contacts to gmail and let the devices sync with the gmail account. This will keep everything in the default data file, just like it is not. Its not free though.