You need to modify this a little bit.
class Organiser extends WP_Widget {
...
function __construct() {
add_action( 'wp_enqueue_scripts', array('Organiser', 'register_plugin_styles') );
...
}
public function widget( $args, $instance ) {
wp_enqueue_style( 'organiserStyle' );
include(dirname(__FILE__)."/organiserWidget.php");
}
static function register_plugin_styles() {
wp_register_style( 'organiserStyle', plugins_url( 'organiser/css/organiserStyle.css' ) );
// wp_register_style( 'organiserStyle', plugin_dir_url( __FILE__ ) . 'css/organiserStyle.css' );
// wp_enqueue_style( 'organiserStyle', plugin_dir_url( __FILE__ ) . 'css/organiserStyle.css');
}
...
}