I think the orderby key is at the wrong place. It think it should be like this:
$args = array( 'post_type' => 'event', 'order' => 'ASC', 'orderby' => 'meta_value', 'meta_key' => 'your key to order', 'meta_query' => array( 'key' => 'Date Ordering Format', 'relation' => 'AND', array( 'key' => 'Event Type', 'value' => '4. take-out tuesday', 'compare' => 'LIKE' ), array( 'key' => 'Past Event', 'value' => 'Past', 'compare' => 'EXISTS' ) ) );