Just dropping by to make an appearance every two months and to add my 2 cents, a completely assembled Eb horn could fit in the right side of that case -- and a fully-assembled Ab sopranino would be swimming in that spot. I do think the horns you currently have are an A and a Bb and I think you might be right that you're missing a C or, for that matter, an A or Bb Boehm system horn. One could then say that one of the empty slots on the left would hold a top joint and a barrel. The other slot on the left might be just for storage. I can't make a good argument for a 4th instrument.
All hypothetical, of course. It's probable you can find a Penzel-Mueller catalog and find out: P-M made a lot of horns and there's a lot of documentation online. It's also possible that it's a non P-M case.