The ordering of the buttons is controlled by how EasySocial is calling the JFBConnect code to insert the buttons.
In /components/com_easysocial/themes/wireframe/facebook/button.jfbconnect.php, around line 20, try replacing
with
{JFBCLogin providers=facebook,linkedin,google,yahoo,windowslive,twitter}
The providers setting lets you put the providers in whatever order, as long as they are configured correctly with API keys. Let me know how that goes. If that works, you'll probably have to create your own theme so that these changes don't get lost if you upgrade EasySocial.
-Melissa