Essentially, you're using classes wrong.

You’ve been using classes statically. That’s really bad…

I’ve moved (almost) everything you need for now into the main class,
PyBot. You should do stuff in there, using self, until it gets too
large, then maybe move some things into another class called
IrcConnection or something, in irc.py.

I also removed your “external” class, I’m not sure why that existed.
The last 6 lines of pybot.py show how a python main file should end.
Run this using $ python3 pybot.py