LogOut button only if logged in in front end menu widget

To add a menu item to the end of a nav menu you can use the wp_nav_menu_items hook. Combine that with is_user_logged_in() and you ought to have it.

function add_last_nav_item($items) {
  if (!is_user_logged_in()) {
    return $items .= 'your login link';
  }
}
add_filter('wp_nav_menu_items','add_last_nav_item');

As far as translation, I assume that qTranslate uses the standard translation functions, but I’m not sure as I don’t use it and as it is a third party plugin that part of the puzzle is off-topic anyway.