Thanks to Charles Goddard for asking some questions and providing the impetus for this Axis2 code. 

Notes:

The Calais URL is a URL of a .NET web-service, optionally containing *several* web-methods. Currently, it only contains a single web-method, named "Enlighten"; still, you must specify the method name in your POST request. (Otherwise, the server has no clue which web-method you are trying to invoke).