There are scripts for mail archival in Microsoft Outlook all over the Internet, but they are not under version control. You cannot send a patch or report an issue on a random page. You can do it on GitHub.
The latest versions of Microsoft Outlook for Mac don't include the script menu. The scripting has to be done in Automator, which requires extra care. You don't want to archive email accidentally, without seeing what is being archived.
With the primitive scripts, Microsoft Outlook would often ignore the hotkey. This script aims to inform the user whenever it's run. If everything is fine, a non-obtrusive notification is used.
Create folder "Archive" under "Inbox" if you haven't already done it.
Run Automator (just click on the Launchpad icon and type "Automator"). Select "Service" in the initial dialog. Choose "Utilities" in the leftmost column. Double click "Run AppleScript" in the second column from the left.
Copy and paste the contents of MacOutlookArchive.scpt to replace the suggested script. Above the script, select: Service receives no input in Microsoft Outlook. Below the script, check "Ignore this action's input".
Select File -> Save in the menu, save service as "Mac Outlook Archive" or any name of your choice. Quit Automator.
Now let's associate the service with a hotkey. Open System Preferences -> Keyboard -> Shortcuts. Select "Services" in the left column, find the service under "General", set shortcut to the desired value.
That should be sufficient to make the script work.
When Outlook starts, it may ignore the hotkey. To work around that bug, check the Outlook -> Services menu in Microsoft Outlook, but don't run anything from it. Just make sure the "Mac Outlook Archive" service is there and associated with the correct hotkey.
Once you see the key in the menu, just close the menu by selecting the main Outlook window with the mouse. The hotkey should start working.
Open Finder. Press Shift-Opt-G and enter ~/Library/Services to open the Services directory. Drag the service to trash.