order by meta_key [duplicate]

Format of this meta is OK – it should work. I’m not sure what you’re doing in this query args, though. You use meta query incorrectly.

If you do it like this, it should work fine:

$my_query = new WP_Query(
    array(
        'author' => $current_user->ID, 
        'post_type' => 'tribe_events', 
        'orderby' => 'meta_value',
        'order' => 'ASC',
        'meta_key' => '_EventStartDate', 
        'meta_query' => array(
            array(
                'key' => '_EventStartDate', 
                'value' => date('Y-m-d') . ' 00:00:00', 
                'compare' => '>='
            )
        )
    ));