Clear data stored with drupal_static() and cache_set()
The Drupal way is to have a $reset parameter to your function.  It would look something like:

function _mymodule_call($reset = FALSE) {
  if ($reset) {
    // do stuff
  }
  // ...
}


node_load() is probably the best example of this.

In your specific case, you can pass the $reset parameter to drupal_static() or explicitly call drupal_static_reset().  For the cache backend, you need to think whether you want to just rework the logic and just do the cache_set() or explicitly call cache_clear_all($cid) (my guess is the former).

And remember, that drupal_static() is only effective when you need the value multiple times during the same request.  This does not persist between page loads (or any other HTTP request that get handled by Drupal).