Several causes and fixes —
This is often due to the hidden .TemporaryItems folder at the root (top level) of a file share not having the correct permissions or not existing, or being symlinked to another storage device.
Use these commands to create the required folder and set the correct permissions on the .TemporaryItems folder
sudo mkdir /Shared\ Items/Share/.TemporaryItems
sudo chown -R 99:staff /Shared\ Items/Share/.TemporaryItems/*
sudo chmod 1777 /Shared\ Items/Share/.TemporaryItems
If this folder already exists and has stuff in it, make sure no one is connected to the server and then remove the contents of the folder. Then set the permissions correctly.
It can also be caused by the finder locking the file as it creates a preview icon or Preview pane view of the file.
This can fix that —
sudo mv /System/Library/QuickLook/Office.qlgenerator /System/Library/QuickLook/Office.qlgenerator.bak ; killall Finder
This problem can also be caused if a Users home folder is on a different drive than the main Macintosh HD and their Caches folder or items within that are symlinked elsewhere (say to /tmp or similar).
The last cause is an overlap between UIDs of users on the local machines and the server.
This can cause one user's Office to think the files are opened by the same user, but they cannot still access the files, at best. At worst, is can cause crashing as word tries to delete and reuse them files in use by another user on another machine.
You will need to check the UID of each user and compare that to the server. If there are mismatches they will need to be created. It can sometimes be enough that every one has a unique ID and there are no overlaps, but it is much better if the local UID also matches the server.
To fix this can be messy — Involving changing the UID on the server and local machine, then ensuring all the users existing files are then chown to the new UID.