Rules of quoting and whose words are they?

Hi everyone!

I've got some serious problem. I'm working on translating a short story, which was wrote in English. The problem refers to rules of quoting – normally we should put a quoting sign on the phrase, which said someone else than the narrator. But the thing is, that the author wrote like that (to give an example): Cathal had gone back to Dublin the night before, she said, but would be down later. She sighed and looked at me. The hospital had phoned, she went on, and things were worse. Your mother, she said, had a stroke during the night, on top of everything else. It was an old joke between us: never 'our mother' or 'my mother' (etc...).

An Irish author wrote this story, and the hero there, who is also the narrator, relate some facts from the past to his friend. There are no quoting marks on the begining of someone else's statement (which is visible above). I clearly understand that the narrator introduces statements, which are not his own, but author of the story does not show this at all. And, eventually, I don't know what to do: to treat the statements of other heroes like a reported speech (because the author doesn't even mark it by beginign from another paragraph) ar like a fully operating quote. Should I start it from another paragraph, place the quoting marks, etc. What would you do? Please, help, if you know how. And thanks a lot!