Im guessing your students wouldnt have the knowledge to use a web based irc client? or be able to install other clients? The students can not just be trusted? i mean, no matter what you do, if they are knowledgable or willing to look into it enough, they will get around it anyway, so your efforts seem somewhat redundant.
If thats not the case, then just turn off the view options for menubar, toolbark, switchbar... create a little script that auto comments them to the private network and channel... add some code (like rock suggested) to prevent some commands being used... and delete the help file.
Personally i think its a waste of time, If they want to get around whatever you do, then they will. If they can browse they will be able to get onto other networks, or infact find help about mirc, or even find a mirc.exe online to replace your modified one with.
On another note: isnt modifying the mirc binary (directly) against the user agreement?
