Thinking about it logically - without touching on any specific technologies - if it's not your machine and you don't trust root then you have a problem.
You really can't do anything about securing
irssi. Root will always have permissions to force the attachment of screen sessions, to sniff IRC traffic from the network or potentially to peek into the contents of process memory.
You could encrypt files with keys and passwords. But it would require the system having access to the encryption keys when required, which in turn means that root would also have access and that they could be attacked with brute force. Unencrypted files would be present in memory or disk for the period of time that they were used, and you guessed it, root can see those too.