Using OS X Server resources on non-Macs I currently have two Mac Mini servers with several Mac clients and everything works well (DNS, Open Directory, Contacts/Calendar/Messaging, File Sharing, Time Machine, etc). I'm open to introducing Windows 7/10 and Linux (Ubuntu/CentOS) into the environment as BYOD option. Mail is handled by two linux mail servers (IMAP only).

Does OS X server integrate into these environments? I'm sure both can join Open Directory, or at least Linux can.

Most importantly, how can I get Contacts/Cal to work across Android/Windows mobile and desktop devices?

OS X 10.10 Server
Server data app on OS X is highly standards compliant. LDAP is industry-standard (but it's not active directory),  Mail is IMAP, CardDAV, WebDAV and CalDAV. All are quite standard and ubiquitous.  Filesharing uses SMB3. 

Unless you have highly specific/rigid client requirements or are wedded to certain client apps, you should be able to make productive use of server.app services across multiple client operating systems.