Hi barrmatt,
Did you get any error messages when Excel or Word crashed?
Based on your description, you have upgraded to the current version of Office.
First I suggest you view the crash report, you can go to ~/Library/Logs/CrashReporter to see if there is a crash log for the application that is crashing.
If a particular application is crashing, you may find a crash log in /Library/Logs/CrashReporter/ or /Users/you/Library/Logs/CrashReporter/.
Crash logs are meant for developers and they are difficult for most users to understand. Hopefully, you can get a clue as to what is causing the problem from the logs that will help find a solution.
And I also suggest you try to reinstall Office for Mac 2016, and update it to 15.13.1.
About how to completely uninstall before you reinstall, please refer to this article:
https://support.office.com/en-us/article/Troubleshoot-Office-2016-for-Mac-issues-by-completely-uninstalling-before-you-reinstall-ec3aa66e-6a76-451f-9d35-cba2e14e94c0
Hope it's helpful.
Regards,
Emi Zhang
TechNet Community Su