Some routers will let you use triggered port mapping. It allows incoming port 113 connections to go to multiple computers on your network. That way you can use mIRC from multiple computers. Triggered port mapping listens for messages from your computers, that have a specific destination port, or range of ports.
For example, you can tell the router to trigger a port mapping when it sees a connection message for port 6667, which is usually how you connect to an IRC server. You also tell the router to map port 113 to any computer that causes the trigger.
Unfortunately some routers don't have the triggered port feature, or it doesn't work right with port 113. I'm not sure why port 113 is such a problem, but please complain to the router manufacturer if they don't support port 113, or it doesn't work correctly.