We have an internal network (not connected to the internet) that we want to use Microsoft Word 2016 to collaboratively edit documents. Is there any way to do this without having a SharePoint server?
From research online it appears the collaboration promised in Office 2016 is not really mature, and really relies on syncing functionality built into OneDrive (and Sharepoint).
You can try using another SVN that supports Office document formats, but native to Word and the other Office 2016 programs, real-time coauthoring functions require the additional capabilities provided by OneDrive and Sharepoint.
Another option some people mention is Sharepoint Foundation, which appears to be a basic version of Sharepoint for small groups that is either low-cost or free.