Leave as is or replace; they're done.

They are already sanded through to the tongues, so in one way they are no longer serviceable, but they can't get any worse.
If they started life at 3/4", they are 1/2" now; that's how much wood has been sanded/walked off.
Casey

I agree with everyone above. cant do too much to these floors. this is the one of the few times where I would suggest carpet over hardwood. its cheaper than replacing the whole floor with new. but as far as saving what you have, no go.

Thanks everyone. That is what I was worried about. I will probably just live with them until I can afford to replace.

Although the damage is only in two small places...The rest of the floor is in pretty good shape. Has anyone had good luck with "feathering" in new or salvaged pieces?

Also, the house was built in 1910. Is it normal for it to have hardwood AND a subfloor? You can see from the basement that there is a subfloor running diagonal. I can't believe these floors would have been anywhere close to 3/4 of an inch, but I suppose they've been refinished a few times over the past 100 years. I've attached a picture from where I took the cold air return out. Very low traffic area in a corner by the built-ins. There has obviously been a piece of subfloor replaced, but that's where I could get the best picture of the actual floors.

Again, thanks everyone! I'm just getting started researching everything and there is SO much conflicting information on the internet!

Thin slat oak flooring in T & G was common over diagonal subflooring in many regions, although it is more common to see thin slat flooring without the tongue in groove and top nailed.

You perhaps can weave in new material to match the old, but you would have to determine specie, grade and sawing characteristics to have that successful. An exact measurement of the slat thickness at the cold air return will tell you the original thickness. Then you go hunting for material to match or have it milled to the size and profile of the existing.

Ideally, if you had a room with this product where you plan to install new flooring, then you could remove it and use it as your weave in material. Or, should you see a house of the same vintage as yours that is slated for demolition, you could pull flooring from that to use in your restoration.

Also, the house was built in 1910. Is it normal for it to have hardwood AND a subfloor? You can see from the basement that there is a subfloor running diagonal

Yes, it was common in many areas. You may have had the extra-thin stuff, which was considerably cheaper.

It's sanded as much as it can be sanded in that first picture. I'd clean it and fill in the cracks with a matching wood filler (there's one made for floors like this, it stays flexible) and then paint it or stencil it until you are ready for replacement.

How wide is each strip and what is the thickness?