Y además las cadenas de caracteres en el SQL deben quedar entre apóstrofos ('):
Código PHP:
$qry = "INSERT INTO users(full_name, ";
$qry .= " first_name, ";
$qry .= " last_name, ";
$qry .= " email, ";
$qry .= " gender, ";
$qry .= " birthday, ";
$qry .= " provider_id) ";
$qry .= "VALUES('$name', ";
$qry .= " '$first_name', ";
$qry .= " '$last_name', ";
$qry .= " '$email', ";
$qry .= " '$gender', ";
$qry .= " '$birth_day', ";
$qry .= " '$microsoft_id')";
$result=mysql_query($qry);