Use mysql's own date functions to format the date:
$result = mysql_query("SELECT *, DATE_FORMAT(birthday,'%W %d %M') AS bday from users WHERE (DAYOFYEAR(birthday)) - DAYOFYEAR(CURDATE()) < '10' and (DAYOFYEAR(birthday)) - DAYOFYEAR(CURDATE()) > 0 ORDER BY (DAYOFYEAR(birthday)) - DAYOFYEAR(CURDATE()) ASC");
Later on you can echo that birthday from $result_ar2['bday']. Aint that neat? 🙂