I was feeling really frustrated for a while. The following brought relief!

Problem & Resolution

• Open MS Word.
• Open File from OneDrive.
• Error:
  • A problem occurred while accessing the Office Document Cache.
  • Do you want to repair this problem?
  • Choose Yes.

• Error:
  • The Microsoft Office Upload Center found a problem while accessing the Microsoft Office Document Cache and needs to repair it before it can continue.
  • As part of the repair a copy of the cache will be saved as a backup and a new cache will be created.
  • Choose Repair.

• Error:
• The action cannot be completed because another application is using the Microsoft Office Document Cache.
• Please close all Microsoft Office Applications or restart your computer and start again.
• Use Task Manager to kill all processes associated with the MS Office Cache (there’s often about three or four). For example:
• Microsoft Office Document Cache Sync Client Interface (this is the usual suspect)
• MS Word
• Microsoft Office Click-to-Run
• OneDrive Sync Engine
• Microsoft Office Document Cache
• Etc
• Choose Try Again.

• If the Browse For Folder window opens (why?), then choose Cancel.

The above did work for me!

See also:

http://www.7tutorials.com/fix-problems-microsoft-office-document-cache-being-corrupted