The OWA My Tasks web part is not an XSLT-based web part, thus there is no answer to that part of your question.
The web part definition of this web part is the following:
<?xml version="1.0" encoding="utf-8"?>
<Assembly>Microsoft.SharePoint.Portal, Version=18.104.22.168, Culture=neutral, PublicKeyToken=71e9bce111e9429c</Assembly>
<Description>Displays your tasks using Outlook Web Access for Microsoft Exchange Server 2003 or later.</Description>
If you wanted to create a custom web part with this web part as your base, you can use the Type Name and assembly referenced in the XML. You may also want to take a peak at that code using .NET Reflector or other reflection tool so you can understand how the web part is structured before getting too deep into it.