I am resisting an overwhelming desire to curse exim4, as I don’t know anything about it and its design will probably make sense once I understand it. However, my goal was extraordinarily simple: I want to be able to send mail from the command line using the `mailx` command. After a good half hour of Googling for results that were useless, with the exception of telling me I probably needed to configure exim4. I never did figure that out with Google. I logged into another host where mailx does work and grepped for the name of my SMTP server. Well, the answer is simple. Edit /etc/exim4/update-exim4.conf.conf according to the comments inside. Then, run the /usr/sbin/update-exim4.conf (yes that’s executable). Don’t forget to also run`/etc/init.d/exim4 restart`.
And maybe, just maybe, I was setting this up for use from a CGI script. Here are the Apache docs on enabling CGI.