The short answer is No.
There are APIs that will (apparently) allow you to parse Outlook "msg" files:
However, turning that into something that will display as a web page is something else. It is not the sort of thing you would implement an API to do. (You might contemplate a reusable JSP to do it ... or something ... but it seems a long shot. And I couldn't spot anything ...)
Maybe you should consider an alternative like OWA where the user's browser talks to the Exchange server directly.