The vinyl tiles require an approved underlayment. They won't stay stuck long, to the pine plywood. Other then that I can't advise you in your thoughts.

OK, I'm confused. Everything I read seemed to indicate that 1/4" plywood IS an appropriate underlayment.

I'm also getting the feeling from my reasearch that they would actually stick better if I put some kind of sealer on the plywood first, the same way that (for example) a kid's sticker would stay put longer on a finished surface than on untreated plywood.

So I'll modify my question to this -- I have 1/4" plywood already down. I want to put self-stick tiles on that as a temporary (6-12 months planned, 2 years absolute tops) fix until we can afford to refinish the wood floors underneath the plywood. What could I do to the plywood to seal it, and what SHOULD I do to the plywood (or put over the plywood) in order to put down self-stick tiles?

An adhesive primer will help the tiles stick to the plywood and help to seal it as well. It's available in gallon jugs in the flooring section, near the vinyl flooring. It won't make the plywood impervious, but it will help.

I had the ultimate cheapie vinyl tiles down over concrete for years. The stuck fine until we had a flood. After that most still stuck but not as good. I will say that some stick better than others. In fact I recall the Armstrong not sticking as well as the junkers I bought.

The ¼" ply, needs to be a hardwood sanded face, usually it is Birch. Pine plywood is made from pine. Pine has pine sap. Pine sap is not a good thing with resilient flooring over the top.

VInyl sheet flooring would be a much better product for this application. Since it's only for a limited time, you could purchase the cheapest thing going and still have it be a continuous sheet over the plywood. However, the issue is going to be the wall/floor joint. Male dogs mark on vertical surfaces, i.e. the wall. This runs down the wall onto the flooring and in between the wall/floor gap. The best solution would be applying preprimed and painted quarter round after the sheet floor installation and then a good caulking job for the joints between the wall/quarter and floor/quarter.

Getting your dog neutered will just about eliminate any marking issues. The testosterone present in an intact dog is usually the culprit for a lot of aggression and possessivenes behaviors. Not to mention it also greatly increases the chance of cancer in your dog to have him remain intact. Crate training and leash/tethering him to you while he is in the home so that he is always under your direct supervision will work to elminate any habit that may remain after the jewels are gone. Treat him like a baby that needs potty training all over again and you'll have a success. Belly bands also help a LOT.

Thanks everyone for the clarification on how to prep the surface before I do this, and the issues with pine.

Live_wire, the dog -- a rescued pug who came to us with this problem -- has been neutered for as long as we've had him (over 2 years), is in his crate when we're not home or while we're asleep, and is in a belly band as much as we can keep him in one (he's a master at getting out of it). We've attempted keeping him on a very short leash next to us to attempt to catch him in the act, we've attempted several different meds to deal with the anxiety behind the marking, basically if the solution has been suggested we've tried it. I appreciate the suggestions, but they've all been seriously tried and failed. It's probably why he ended up in rescue.