I'd be checking any and all scripts that you run & that the bot uses (I'm not familiar with eggdrop) for lines that allow a non specific entry...for mIRc, they would look something like one opr more of the following

on *:text:*:*
on *:text:*:#
on *:text:*:?
on *:action:*:*
on *:action:*:#
on *:action:*:?

Lines like these are extremely supseptible(sp?) to commands that can be entered which can cause a lot of problems.

If you have any code that is like that, then I would recommend that you see about getting that script (or those scripts) re-written.

I don't know how they did it, but the above shows how they might've been able to pass a command to a script which, in turn, granted them ops. The above also shows the primary method of preventing this.