By far the most likely explanation is that you have a trojan (a type of virus) that is launching mIRC when you start up your computer. mIRC then connects a drone to an IRC network which then can be used later by an lame abusive user to attack websites/users/companies/etc. Basically, using your computer to attack others.
Press CTRL+ALT+DEL and terminate mirc.exe if you see it, also check the Processes list.
Scan your computer with a good Antivirus/trojan cleaner, examples can be found in this thread
. Use more than one, no one virus scanner can detect everything.
Make sure that you don't download files if you don't know what they do, visit websites that aren't trusted or unknown to you, or open email attachments you get in emails from unknown senders.