For the last two days I have been searching for an answer to this question.
There is no specific SOAP support in Enyo. You could likely find another JS library supporting SOAP and wrap it up in an Enyo kind.
Enyo 1.0 has a Web Service kind.
Enyo 2.0 currently just exposes an Ajax control to use instead.
If you decide to use something other than SOAP, I'd recommend the service return JSON. If you must use SOAP, you'll need to extend Enyo yourself to support it.