How old are my children? (*)

A census-taker asks a woman for information about her children. She says “I have three children, and the product of their ages is 36. I would tell you the sum, but that wouldn't help you.” The census-taker replies “But then, you haven't given me enough information - you have to tell me something more.” The woman says “OK - I'll tell you that my oldest daughter likes to play the piano”.

What ages are the woman's three children?

Bonus points for spotting the four (or more) ambiguities that mean this problem has multiple answers.