Oxford obsessive?

I’m starting to see Oxford commas in my sleep. In related territory, I recently came across:

Does that mean either sherry or balsamic vinegar or sherry vinegar or balsamic vinegar? Impossible to tell.  A friend suggested a ‘sort of Oxford comma’:

1tsp of sherry, or balsamic vinegar

Well, it’s unambiguous. Wrong, admittedly, but you can’t have everything…

In other news:

‘He was accompanied by a Hungarian, a nice chap, and a painter’

How many companions did ‘he’ have? One, two, or three?