'Irish logic' is where things are backwards, in a specific way. It's kind of a single mindedness. Usually it's a misunderstanding-based joke, not exactly stupidity, but a silly perspective. E.g. it takes more Irishmen to change a light bulb because one holds it and the others swing the ceiling round.
I'm first generation Irish immigrant, and my family loves these kinds of jokes, we don't see it as hateful. But I wouldn't tell them around any old Irish person.