Oscillodyne?

[leadlike]

It doesn't look like a common 20's battery set to me, either. I think superhets typically had 8 tubes (usually 199s). But the tuna fish can transformers scream superhet. Post this on ARF, someone there will know what you have.

Yep, get some 01as, and you can probably use a 71 tube for the audio output.

Did you check the underside? Sometimes there are elaborate instruction cards tacked there.