you'll want to look at the following events:
as well as Halting Default Text. All of this can be found in mirc's help file. If you find another type of message, look for an event that triggers it in mirc. If not, you can always ask on this forum how to halt specific text from showing in your specific #channelname.
Open a second instance of mirc and set the color scheme different from your main mirc, and have it only show your text in channels by color coding everything else as the same colors as your background. If you do this, you'll need a completely separate copy on your hard drive (because you can only have one active color scheme that I am aware of). While this wont disable those messages, it will hide them. Depending on your level of scripting, this might be easier. The problem with this is if you only have one nickname on that network, you can't use it in both mircs at the same time, so may need to have another nickname added to the bot's list of authorized users.
If I missed anything, or stated something incorrectly, forgive me, and Im sure others will correct my missteps.