With the debug window I could more or less identify that it happens right after joining all the channels (I tried to reproduce opening a new instance of mIRC, but it gets so slow that I can't click the debug window before it starts freezing, and it changes to the joined channel window every time it joins a channel).

I'll do some more tests later, but looks like that running mIRC with the debug mode helps with the problem (sometimes it's not even sluggish at all, dunno why)

Code:
06:47:47 <- :weber.freenode.net 324 nickname #channel +cnt
06:47:47 <- :weber.freenode.net 329 nickname #channel 1398296480
06:47:47 <- :weber.freenode.net 324 nickname #channel-community +cnt
06:47:47 <- :weber.freenode.net 329 nickname #channel-community 1497620975
06:47:47 <- :weber.freenode.net 324 nickname #channel-dev +cnt
06:47:47 <- :weber.freenode.net 329 nickname #channel-dev 1400515215

Very strange. It looks network related but it doesn't affect my internet connection, it affects the entirety of my OS.