Q. How can I remove Office from a machine that is not cleanly uninstalling?
A. Microsoft has an Office Scrub tool. This tool can be used to remove all elements of Office from a machine even in instances where Office is not available from Add/Remove programs. To download Office Scrub navigate to https://support.microsoft.com/en-us/kb/971179 and download the version required based on your version of Office and Operating System.
Once downloaded you will have an OffScrub<version>.vbs file. If you run with no arguments then you will be prompted for which components to remove however it's also possible to use in an unattended mode. For example to uninstall Office 2010 use:
cscript OffScrub10.vbs ALL /Quiet