I have option to install an Office package to 5 machines. And I already have one copy on my work laptop.
I wonder is there a way to install it on my private computer which is used by other people as well, but disable access to recent documents, Sharepoint and OneDrive?
You might need to consider having your own account on that shared/private computer, to protect the content.
Or, it may be acceptable to you, to "switch account" or "sign out" of Office (ensuring that you have not "stored/saved" your O365 userid/password).e.g.:
http://www.akspug.org/Blog/Post/71/Office-365,-Office-2013,-and-Account-Switching
I'm not sure if this would periodically (30 days?) require you to sign-in to Office on that computer, to re-validate your O365 subscription..