Restrict page to members only does not work for page ID, slug or page title

The init hook is called too early for your needs. And you should use wp_redirect(). Try this:

function contactusnot() {
    if ( ! is_user_logged_in() && (is_page( 220 ) || is_page( 'Contact us' ) || is_page( 'contact-us' )))  {
       wp_redirect( 'https://google.com/' ); 
       exit;
    }
}
add_action( 'template_redirect', 'contactusnot' );