If you have Windows 98 or ME (meaning that it's not easy to check your processes), open drwatson.exe (it should open from anywhere, since its directory should be in the PATH system variable), then double-click on the icon that appears in your taskbar, and a dialog should open.
Go to View and click on Advanced View, and then click on the Tasks tab; check for any tasks that have mIRC as their description (and mIRC Co. Ltd. as their manufacturer). If you find any, check their Path (this is where the executable is stored).
Now you can delete the executables and/or disable them from running on Startup. You can do the latter by opening msconfig.exe and going to the StartUp tab. Once there, just uncheck the applications you want to disable.