How to find out what email program is running on my server.

Try running telnet localhost 25 on the server. The mail server should reply saying what software it is. For example, sendmail would reply with this:

$ telnet localhost 25
Trying 127.0.0.1...
Connected to localhost.
Escape character is '^]'.
220 zeus.example.com ESMTP Sendmail 8.14.4/8.14.4; Tue, 24 Jul 2012 23:37:32 -0500

If that doesn't work you can run ps -ef to get a list of running processes, and look through the list for exim, sendmail, postfix, etc. You can pipe that to the grep command to search for a particular process, like this:

$ ps -ef |grep sendmail
root      1672     1  0 Jun10 ?        00:00:39 sendmail: accepting connections       
smmsp     1675     1  0 Jun10 ?        00:00:00 sendmail: Queue runner@00:25:00 for /var/spool/clientmqueue
root     13028  1672  0 21:37 ?        00:00:00 sendmail: server localhost [127.0.0.1] cmd read

You could also run netstat -lpnt and see what's listening on port 25

netstat -lpnt
Active Internet connections (only servers)
Proto Recv-Q Send-Q Local Address           Foreign Address         State       PID/Program name
tcp        0      0 127.0.0.1:25            0.0.0.0:*               LISTEN      2026/master     
tcp6       0      0 ::1:25                  :::*                    LISTEN      2026/master    

In this case postfix shows as master

Thank you Agwa, that was very helpful.