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I've got my work light underneath on the left so you can see better. There's a matching set on the right side that aren't lit up. They are shaped like a figure 8 (upside down in this view) meaning that it looks like someone put a small hole in, then decided they needed it bigger and offset. all 4 holes have this same size/shape.

First thing, any clue what these were for? Looking underneath, it appears that something was attached underneath, but the cars are so low I can't imagine what was attached.

Second, what would you do to plug them? I'm trying to prepare for the return of the rain (this is a DD). I was planning on just using some conical rubber stoppers, but the oblong shape is going to make that a non-starter. I'm afraid any kind of tape will just hold water and be worse than nothing at all. Is nothing at all my best shot?

It would be a real shame to let rust get started, it's in such great shape now.

If you don't want to weld them (the proper method) you could do the old beer can and black RTV silicone method. Cut patches out of an aluminum beer can and stick them in place with the RTV. Ghetto, but it works and they will peel off when you get a chance to weld them up proper.

Or fender washers on both sides bolted with silicon temporarily.

Geez, how about some used chewing gum

Not sticky enough

Really, what's better if you don't have the time, money or equipment to weld it up proper? Just leave it to hose the trunk? Or put a temporary patch till you have the time or dime to fix it proper.
I did this on the wifes bug, big freaking gas heater exhaust hole. I never did fix it proper, lasted 5 years of Canadian winters. The whole bug rusted right out, but the patch (which BTW was directly above the front tire) never failed.

Rust doesn't start because there is a hole, it starts on unprotected metal. Clean up around the holes, prime, paint and find some rubber plugs. A round plug in those oval holes will most likely seal better than your front hood gasket anyway.

I agree, don't use rtv silicone. Just paint it to seal it and put a rubber plug in it.

Put a nail in a jar with a glob of rtv and put the lid on it. After a day you won't want to use rtv on your car anymore. If you don't have seam sealer just use regular latex caulking for the short term. It will last for years.

You could use a step drill and make the holes round to the size of a rubber plug.

Just buy a midget and have him stuff his fingers and toes in the holes. Won't rust. Won't fall off. And when your done driving, have some fun with him and Dr. Evil