Order By table field comment_status in WordPress > 4.0

Here’s a way to add an extra Comment Status field to the posts list table:

add_filter('manage_post_posts_columns', function ( $columns ) 
{
    $_columns = [];

    foreach( (array) $columns as $key => $label )
    {
        $_columns[$key] = $label; 
        if( 'title' === $key )
            $_columns['wpse_comment_status'] = esc_html__( 'Comment Status', 'mydomain' );
    }
    return $_columns;
} );

add_action( 'manage_post_posts_custom_column', function ( $column_name, $post_id ) 
{
    if ( $column_name == 'wpse_comment_status')
       echo get_post_field( 'comment_status', $post_id );    

}, 10, 2 );

Here’s how we can add a support for comment status ordering through the posts_orderby filter:

add_filter( 'manage_edit-post_sortable_columns', function ( $columns ) 
{
  $columns['wpse_comment_status'] = 'comment_status';
  return $columns;
} );

add_filter( 'posts_orderby', function( $orderby, \WP_Query $q ) use ( &$wpdb )
{   
    $_orderby = $q->get( 'orderby' );
    $_order   = $q->get( 'order' );

    if( 
           is_admin() 
        && $q->is_main_query() 
        && did_action( 'load-edit.php' )
        && 'comment_status' === $_orderby 
    )
        $orderby = " {$wpdb->posts}.comment_status " 
            . ( 'ASC' === strtoupper( $_order ) ? 'ASC' : 'DESC' )
            . ", {$wpdb->posts}.ID DESC ";

    return $orderby;
}, 10, 2 );

where we sub-order by the post ID.

Here’s an example output:

PS: Since WordPress 4.5 (#35601) it’s possible to filter WP_Query by comment_status and ping_status, so you should be able to implement such filtering for your the posts list table, as well