Welcome to the Workshop community @debralea5. I'd be more than happy to answer your question.
Let me start by saying what a unique property you have there. I have to admit I really like the timber panelling, but agree painting could give the areas a much more modern look.
You can paint plywood walls, but the question is more-so "Can you paint over a gloss timber coating". The answer is yes in both cases, though there is prep work to be done. You can follow this step by step D.I.Y tutorial which involves sanding the gloss layer of the coating off.
The other more time and labour efficient process is to use a primer that will stick to the gloss surface. For this, I would recommend Rust-oleum B.I.N Primer Sealer Stain Killer, as it is a shellac-based, works over or under any topcoat and sticks to glossy surfaces. You will need to use a oil-based topcoat to paint the walls after the priming coat.
Please let me know if you require further information about the product, the process or have any other questions.
It's my pleasure to assist in your project. You'll also see that we have plenty of creative and helpful community members on Workshop, they contribute their own projects and advice here every day. I'm sure together we will be able to guide you through the whole process.
We look forward to you starting this project and seeing the end results.
If you have any further questions or queries, please let me know.
I'd paint. You would still have the texture of the timber panels but it would really lighten the rooms. That hallway looks particularly dark.