They are pronounced differently, indeed.
Oni sounds what Czechs call "soft' sound kind of as if the N had an accent over it, but it does not need it as it is followed by I. And that makes the sound Ň. https://forvo.com/search/oni/cs/
Ony has a 'hard" sound. https://forvo.com/search/ony/sk/ (yes, this is a sample of slovak, but the czech one on forvo sounded weird and in this case czech and slovak are the same).
I wondered whether that might be the difference. I was also wondering whether the i and y might be different the way they are in Polish and Ukrainian (i and и) but it sounds like the vowels really are the same, which is what I seemed to recall from a summer of Czech two decades ago.
My daughter and I were just talking about that the other day. Written French makes a great many distinctions that are simply not pronounced in the spoken language, so while you should be very careful in distinguishing "elle mange" from "elles mangent" in writing, in the dialects of French with which I am familiar, there is no difference in pronunciation. My daughter asked me how spoken French could deal with such ambiguity, but I pointed out that Japanese verbs don't vary by person and they don't use subject pronouns most of the time.
Ona is also neuter plural. More information on the declension of personal pronouns is available at this link: https://en.wikipedia.org/wiki/Czech_declension#Personal_pronouns.