Using the WebDAV search method you can query an Exchange store for items with content type taskfolder.
Updating items with the WebDAV protocol is accomplished either using an HTTP PUT operation for files, or by using the PROPPATCH method for items only containing properties. Since task items not necessarily are associated with files I assume you must use the PROPPATCH method to create items in the taskfolder.
Update: as of Exchange 2010, the WebDAV protocol is no longer supported. Instead, a web service API is available. Here's an example on how to get a Task item.
Clarification: the web service api was introduced in Exchange Server 2007.
To detect which Exchange version you're talking to I suggest doing a "probing" approach. Try some essential web service calls to detect 2007 and 2010, preferably using the Autodiscover
operation. If these do not work, probe the WebDAV interface for earlier versions.