$order = new WC_Order( $post_id );
If you
echo $order->id;
then you'll be returned the id of the post from which the order is made. As you've already got that, it's probably not what you want.
echo $order->get_order_number();
will return the id of the order (with a # in front of it). To get rid of the #,
echo trim( str_replace( '#', '', $order->get_order_number() ) );
as per the accepted answer.