Can any one suggest how I can call the Users default controller's methods, like activate or any other, that I have created in User controller of Admin site with argument?
You would not call the controller methods to activate a user as this would then set a redirect as well - you need to be calling the model. Basic PHP, not really Joomla related.
So you would first include the model
include_once JPATH_ADMINISTRATOR . '/components/com_users/models/user.php';
and then instantiate the object:
$usersMdl = new UsersModelUser();
define your array of user ids to activate (as only variables can be passed by reference):
$myIds = [1, 2, 3];
and then call the models methods:
where 1,2 and 3 are the user ids you want to activate.
(code tested and working in Joomla 3.4+)