Спасибо за помощь!
Где и когда?

Таки нашел решение!

Только не exim, а msmtp:

# cd /usr/ports/mail/msmtp
# make install clean -s
# rehash

Создаем лог файл и конфиг:
# touch /usr/local/etc/msmtprc
# touch /var/log/msmtp.log

Вносим в /usr/local/etc/msmtprc параметры:
account default
logfile /var/log/msmtp.log
domain mx ...

Да:
daemon_smtp_ports = 25 : 465 : 587

# sockstat -4
USER COMMAND PID FD PROTO LOCAL ADDRESS FOREIGN ADDRESS
mailnull exim-4.80. 17364 3 tcp4 *:25 *:*
mailnull exim-4.80. 17364 4 tcp4 *:465 *:*
mailnull exim-4.80. 17364 5 tcp4 *:587 *:*

Попробовал через SMTP - exim вообще не получает письмо
<?php
include('SMTPconfig.php');
include('SMTPClass.php');
if($_SERVER["REQUEST_METHOD"] == "POST")
{
$to = 'vasya@domain.com';
$from = 'no-replay@'.$_SERVER['HTTP_HOST'];
$subject = 'Отзыв';
$body = $_POST['goods'];
$SMTPMail = new ...

Поменял скрипт:
<?php
if ($_SERVER['REQUEST_METHOD']=='POST') {
$name = $_POST['username'];
$phone = $_POST['phone'];
$address = $_POST['address'];
$notes = $_POST['notes'];
$email = $_POST['email'];
$goods = $_POST['goods'];
$from = 'no-replay@'.$_SERVER['HTTP_HOST'];
$headers = 'From ...

Прописал авторизацию.
Лог exim'a:
2013-12-06 11:12:06 1Vonhu-0002Ya-4L <= www@mx.hosting.com U=www P=local S=555 from <www@mx.hosting.com> for vasya@domain.com
2013-12-06 11:12:06 1Vonhu-0002Ya-4L => vasya@domain.com R=smarthost_relay T=smarthost_smtp H=192.168.1.1 [192.168.1.1] X=TLSv1:AES256-SHA ...

Есть продвижения, не большие :-D :
Лог exim'a:
2013-12-06 10:33:46 1Von6o-0002Vs-El <= www@mx.hosting.com U=www P=local S=555 from <www@mx.hosting.com> for vasya@domain.com
2013-12-06 10:33:46 1Von6o-0002Vs-El ** vasya@domain.com R=smarthost_relay T=smarthost_smtp: SMTP error from remote mail ...

Так же, ML1 не видет такой домен
[06/Dec/2013 15:45:30] Message from IP address 192.168.1.2, sender <www@mx.hosting.com> rejected: sender domain does not exist

Лог exim'a:

2013-12-06 09:42:04 1VomIm-0002Q5-A1 <= www@mx.hosting.com U=www P=local S=555 from <www@mx.hosting.com> for vasya@domain ...

Заполнил. Теперь в логах:
2013-12-06 05:19:04 1VoiCG-0002E2-GM <= www@mx.hosting.com U=www P=local S=559
2013-12-06 05:20:20 1VoiCG-0002E2-GM sentry.domainbank.com [64.85.73.28] Operation timed out
2013-12-06 05:20:20 1VoiCG-0002E2-GM == vasya@domain.com R=dnslookup T=remote_smtp defer (60 ...

Вот конфиг exim'a:
######################################################################
# Runtime configuration file for Exim #
######################################################################


# This is a default configuration file which will operate correctly in
# uncomplicated ...