you are correct sir/madam, you could use something like this in your mirc to LOGOFF:
/run c:\windows\system32\logoff.exe
BUT if ya wanna shutdown, like the original poster wants, then ya have to use something like:
/run c:\windows\system32\shutdown.exe -s -t 01
the -s tells the computer to shutdown, the -t sets the timeout in seconds to 01
that is if he has an XP system, if he has a windows 95,98,ME, then he needs to use:
/run C:\windows\rundll.exe user.exe,exitwindows