How to change custom post order ASC/DESC menu_order wise dynamically?

You can hook pre_get_posts and use the order_by argument of WP_Query.
From a plugin or functions.php of active theme, something like the following (untested example):

add_action( 'pre_get_posts', 'my_post_type_sort', 10, 1);

function my_post_type_sort( $query ) {
     if ( is_admin || ! $query->is_main_query() ) {
        return;
     }
     if ( $query->get('post_type') !== 'name_of_post_type' ) {
        return;
     }
     $query->set('orderby', array( 'menu_order' => 'ASC') );

}