Use media queries to test the orientation, in the portrait stylesheet hide everything and show a message that the app only works on landscape mode.
<link rel="stylesheet" type="text/css" href="https://stackoverflow.com/questions/10975387/css/style_l.css" media="screen and (orientation: landscape)">
<link rel="stylesheet" type="text/css" href="css/style_p.css" media="screen and (orientation: portrait)">
I think is best aproach