I've done this before. The procedure is relatively simply as long as your shell account that you are logging into allows port forwarding.
Open putty and load the settings for your shell. Then, in the options on the left, go all the way down to 'Connection' > 'SSH' > then 'Tunnels'
In the 'Source Port' text box, put in a port number that you wish to use. (I use 6007) then put the server you wish to connect to (in domain:port format) in the 'Destination' text box. Leave 'local' and 'Auto' option buttons on. Then connect to the shell.
If port forwarding is allowed on the shell, just open mirc and connect to either localhost:6007 (or, whatever port you used) If that doesn't work, get the lan ip of the machine (easy way is via cmd, ipconfig) then connect to that on the port you used.
If all is good, mirc will connect to the irc server you chose as the destination. The connection may be slow (depending on the connection which the shell server is running on) but is manageable. mIRC will behave as if its really connected to the server, it wont know the difference. (though, iirc, $server and $serverip and similar identifiers will see your local address as the server's address)
For more, see
Here (Putty Documentation) I did this to get around school firewalls when I was in highschool :p
(note: directions are for the latest stable build of putty)
