Well, I definitely do not have any Irish blood, but other than that, I have pretty much all the blood you could imagine... my dad is a pure blooded czech, and the family is tracked down to the 16th century, still Czech.
My mother however, had Jewish parents, the grandmother an Askenazi, she was from Poland, but she considered herself Czech. The Jews always moved around, so her ancestry probably comes from Russia before that and during the course of the last two thousand years, they must've come from ancient Palestine - otherwise they couldn't be Jewish.
The grandfather was from Hungary. He died when I was two. He was a Sefardic Jew, and that means his ancestry came to Europe from Gibraltar in Spain, and must've crossed north Africa sometime in the last two millennia, coming from, where else, Palestine.
I have no idea how orthodox the two Jewish families were, so I do not know whether or not they picked up local DNA on the way.
I consider myself Czech, but I do respect and am aware and proud of my Jewish heritage as well.