Omega Theme: how to change the stacking order of each region for each layout?
The browser, not the server, knows the width of the layout. So you cannot change the stacking order on the server side and move the regions or zones up and down without having the browser talk back to the server, which Omega doesn't do.

You could use Javascript to move things around, which is painful. You could also duplicate the content you want to be in the different places, and then hide it or display it with display: none and display: block. But then you are outputting multiple copies of the content and lengthening page load time.

Here's a similar discussion about (not) changing stacking order in Omega: http://drupal.org/node/1343798.