Just a little fun fact: in Polish, the most common exclamation of pain is exactly the same: Au! or Aua! (often used with prolonged vowels, both in speech and in script, if the pain is sharp, strong and long. It changes into a sort of wailing then: Auuu! Auaaa!").
It can also be Auć!, but that version is a bit more childish (I think), so it's mostly used by parents or grandparents to comfort a child who has tripped, fallen and scratched its knee or bumped its head (for example: "Auć, to musiało boleć!" - "Ouch, it must have hurt!) or to express empathy towards your friend who has just told you some sad or bad news (but nothing too seriosly sad or bad). Adults can say auć to express their own pain too, but it's usually said after just a small scratch which doesn't really hurt much (such as accidently pricking your finger with a pin or a needle), or it's used metaphorically to express some mild emotional irritation (for example, muttering "Auć! O nie!" - "Ouch! Oh no!" under your breath while thinking: "Oh no, I did it wrong! I made a mistake! I answered the last test question incorrectly!" while you're going back home after your university classes) etc.
Is this exclamation used in all those ways in Finnish too? To express physical pain, emotional irritation and empathy towards others?