It is a chat “room” that has absolutely nothing to do with The Straight Dope. I have never been there. I don’t even know how to get there. (I don’t go to chat rooms.)
I am sure that someone else here can give you proper directions to the place if you want to go there.
mIRC is to IRC what Internet Explorer 5 is to the World Wide Web, a client that allows you to interact with part of the Internet. It is free to download and trial for 30 days and costs $20 US to register thereafter. Undernet is an organisation that provides the IRC equivalent to a web server host (Think geocities). #Straightdope is the equivalent to a site hosted on these servers.
OK I have simplified a few concepts in there but the links provided should clarify any questions you have.