How to create a module wide variable that refreshes every page load?
The variable_set() and variable_get() functions are made to set/get a persistent variable. So they should not be used to persist data within a single page request. The drupal_static() function is made for this task and is well documented. Off course, you could also go with a static variable without bothering about drupal_static(). But drupal_static() will make your code more maintainable and future proof.

/**
 * Set or get the shared foo variable.
 *
 * @param $new_value
 *  (optional) If set, the new value to assign to the foo variable.
 *
 * @return
 *  The value of the foo variable. If $new_value is set this would be
 *  the previous value.
 */
function MODULE_foo($new_value = NULL) {
  $value = drupal_static(__FUNCTION__, NULL);
  $previous_value = $value;
  if ($new_value !== NULL) {
    $value = $new_value;
  }
  return $previous_value;
}