If else with shortcodes

This is rather a simple PHP question and almost off topic. You can simplify your code drastically:

$metas = array ( 'twitch', 'own3d', 'livestream', 'ustream', 'justin' );
foreach ( $metas as $meta )
{
    $value = get_post_meta( $post->ID, $meta, TRUE );
    if ( $value )
    {
        echo do_shortcode("[livestream type="$meta" channel="$value"]");
        break;
    }
}

This will run over the list of possible meta fields and stop if it finds one with content.

I wouldn’t use do_shortcode() like this. Use the shortcode handler function instead (the function that is called by this shortcode) to speed the processing up.
Use do_shortcode() only if you have content outside of the shortcode.