How to get tags only with custom meta field and display them randomly?

You can get custom fields randomly using the below code that you can combine with your existing code to get desired output.

function wpll_get_popular_nodes() {
    global $wpdb;
    $custom_fields = $wpdb->get_results( "select DISTINCT meta_value from $wpdb->postmeta pt LEFT JOIN $wpdb->posts p ON (pt.post_id = p.ID) where meta_key LIKE 'tax_image_url_universal' ORDER BY RAND()" );
    if ( is_array( $custom_fields ) && ! empty( $custom_fields ) ) {
        $count=0;
        foreach ( $custom_fields as $field ) {
            if ( isset( $field->meta_value ) ) {
                $count++;
                echo $field->meta_value;
            }
            if( $count >4 ) break;
        }
    }
}