Bob,
Don't use oak for the main carcass of the cage. With all of its grain and texture an extremely dark finish does not look all that great. I have seen finishes where people have troweled plaster of paris into the texture, sanded it smooth, and then stained it really dark. This can look neat and would probably look neat inside of a snake cage, but I don't know much about it. The results also tend to be hit or miss.
If you really want oak you can build the cage's face frame out of it.
With even a lower quality birch plywood you'll have a much better surface for either paint or piano finish. You could try stain, but in this case is that birch laminated ply does not accept stain evenly and this looks bad with a darker stain.
I would instead look into a gel stain or aniline dye.
Regarding piano finish, I don't think you'd need a top coat of poly. I believe it's a durable finish on it's own.
Also, there are other paints that will likely give equal protection to an oil-based poly. Even if they are a little bit weaker they will be easier to touch up.
A semi-refular on this forum uses a black marine enamel over birch laminated ply in his cages. Let me try to think who that is.