Three valid ways to exchange data through a Pega Web Mashup include using the data-pega-event-onpagedata attribute to configure the default value for the gadget, using an action object configured as a script to perform additional actions on a web mashup gadget, and using the Javascript function doAction() to set or read data values through the hosting web page. SQL calls and queue processors are not typically utilized for data exchange in Pega Web Mashup scenarios.