//Our custom sitemap which reads the menu order using extended menu walker class
//Shortcode
function wdp_shortcode_sitemap($atts){ //[sitemap]
	extract(shortcode_atts(array(	
	), $atts));		
	//call the function
	$shortcodecontent = wdp_sitemap();	
	
	return $shortcodecontent;
}
add_shortcode('sitemap', 'wdp_shortcode_sitemap');

//call the menu and use our custom walker
function wdp_sitemap(){
	return wp_nav_menu(array('theme_location' => 'primary', 'walker' => new wdp_sitemap_walker(), 'fallback_cb' => '', 'echo'=>false)); 	
}

//extended navigation class for sitemap rendering
class wdp_sitemap_walker extends Walker_Nav_Menu
{
      function start_el(&$output, $item, $depth, $args)
      {
           global $wp_query;                     
           $indent = ( $depth ) ? str_repeat( "\t", $depth ) : '';    		   		  
		   $id=strtolower(str_replace(" ","-",$item->title));
		   $id=str_replace(array('&','&'),"",$id);
		   $id=str_replace('--',"-",$id);
           $output .= $indent . '<li id="sitemap-'. $id . '"' . $value .'>';		   
           $attributes  = ! empty( $item->attr_title ) ? ' title="'  . esc_attr( $item->attr_title ) .'"' : '';
           $attributes .= ! empty( $item->target )     ? ' target="' . esc_attr( $item->target     ) .'"' : '';
           $attributes .= ! empty( $item->xfn )        ? ' rel="'    . esc_attr( $item->xfn        ) .'"' : '';
           $attributes .= ! empty( $item->url )        ? ' href="'   . esc_attr( $item->url        ) .'"' : '';           

            //$item_output .= $args->before;
            $item_output .= '<a'. $attributes .'>';
            $item_output .= $args->link_before .$prepend.apply_filters( 'the_title', $item->title, $item->ID ).$append;
           // $item_output .= $args->link_after;
            $item_output .= '</a>';
            //$item_output .= $args->after;			
            $output .= apply_filters( 'walker_nav_menu_start_el', $item_output, $item, $depth, $args );
        }
}

Use a shortcode [sitemap] to render a sitemap ordered by custom menu order (Wordpress 3+).

Wordpress custom sitemap shortcode following custom menu order

wordpress, order

PHP