The mso in mso-whatever refers to Microsoft Office. Someone may have composed the message in Word and pasted into Thunderbird, or it may have been edited in Microsoft Outlook at some point.

That still doesn't explain why the message display is corrupted because most programs simply ignore tags/properties they can't understand. There probably is some other problem with the message that is causing the HTML portion of it not to be rendered normally.

If I save the email as an .html file, I can open it in almost any program except Thunderbird and it renders correctly.

Thunderbird sanitized HTML that is renders to block unsafe actions from the HTML source. However without seeing the actual source it is difficult to comment on your specifics. I have found that anti virus products have a nasty habit of corrupting HTML as the scan messages.

The last similar source I saw the mailer was placing everything in the head section of the HTML