You do not need to forward the connection ports (6667, etc). You will need to forward the same ports in the router as what you have set up in mIRC's options. You can change the default 1024-5000 range to anything you'd like (within appropriate port numbers, of course). Usually, a range of 10 ports is plenty.
Alt-O > Connect > Options > Advanced -- Set up your ports that you'd like to use for DCC (chat/send), then forward those same ports in your router. You'll probably also want to forward port 113 for identd. All should be TCP ports (not UDP).
http://www.portforward.com/ has all of this for you with pictures and everything if you'd like to get a step-by-step look at doing it on your particular router.
