Internetworkers: http://www.ibiblio.org/internetworkers/

[Greg Cox <glcox AT pobox.com>]

> assuming that the mail server and the web server are one and the same and
> that one has ssh access to the server, is there any command to discern
> whether said server utilizes IMAP?

If it's up and running and on the standard port,
  telnet localhost 143

If it's up and running and on a non-standard port,
  lsof | grep LISTEN
  and then look for it.

If it's not running but you think it might be there,
  find / -type f -name "*imap*" -print

> what are all the Unix system "divination tools"?

Not quite sure if this covers what you want, but,
beyond yours, what I consider major research tools:

df, ls, uname, find, file, nmap, lsof, diff,
telnet/ssh/openssl s_client, which, ifconfig