I would probably use 'and' for the second clause, like this:
Bob is eating cheese, while John is playing the piano, and Sarah is drawing.
Or, your second suggestion could be appropriate as well:
Bob is eating cheese and John is playing the piano, while Sarah is drawing.
Either one would convey the sense of three people performing separate activities at the same time. Your second suggestion would be especially appropriate if the actions of Bob and John are more closely related (and perhaps Sarah is off by herself drawing).
Using 'while' twice seems awkward to me, but not necessarily incorrect. In the right context, it could be appropriate. In a play, for instance, I could imagine an exasperated parent looking around at his or her children, who should be doing their chores, exclaiming,
Bob is eating cheese... while John is playing the piano... while Sarah is drawing!
But in most cases, perhaps all, I would avoid the double 'while.'