It's odd that Julia or Wille never asked him how he was turned, it was never really hinted at prior to 1795
Oh, I'm sure they asked--but whether or how Barn answered is another story altogether! I'm sure he kept as much of it as possible from them for as long as possible.
I'm pretty sure that some time after the 1795 story, as Barnabas grew to trust and rely on Julia more, he told her little bits of the story, but never the complete version. At some point, there's a scene with the two of them having a confidential conversation in the mausoleum. (Well, doesn't EVERYBODY have their confidential conversations in a mausoleum??) I don't remember any of the dialogue, but as the scene opens, we can infer from what Julia says that Barnabas has finally told her the whole story of Josette and Angelique and how A. made him a vampire. I wish I could remember what else was happening at the time. Maybe it was when Barn was trying to decide whether to go through with Dr. Lang's experiment. Or maybe it was when Cassandra appeared on the scene and he recognized her. Of course Julia would want to know why he reacted so strongly. I suppose it's safe to say that by that time Willie was also aware of most of the story, if not all the details.