My floors are terribly scuffed.
How can I fix them without having to sand and stain my entire house?

You can be an artist to blend the old floor color with your spot finishing. The old finish may have been a linseed oil type of varnish that got dark over time, masking the grain of your oak floors. Modern finishes will let you see the grain much more. After you have prepared the old floor finish by cleaning with a wood floor cleaner you will be ready to try to match the color. I would suggest using shellac with some color in it because it will stick to most older finishes and dries really fast so you can see the results soon after you apply it. After you match the color in the few worn areas, you should use a modern finish to protect your work. Some floor finishers will use clear shellac, the de-waxed kind, as a seal over old finishes and then coat with a water-based poly-urethane to protect the floor from wear.

Thank you so much for your reply! Much appreciated. One question for ya. Would the poly be super obvious in the areas that I spot fix in comparison to the rest of the old floors? Is there a way to blend the new poly with the existing finish better? I ask this because I had sanded and stained our closest floors that were the original wood covered with laminate and even with a satin poly you can tell a huge difference between old and new. So what type of poly finish would be best since the satin is too shiny?

Once you get the color close you will need to seal the area so the wood will not be bothered by spills. Satin poly-urethane is shinier than matte poly. After the coat has dried for a few days you can still dull the surface more by making fine scratches by scuffing with steel wool.Since the old part of the floor has worn so much it needs some protection from foot traffic. Since you are putting so much work into the floor, I would think that you would take the time to coat the whole floor with two coats. At least then it will have the same gloss level. One coat of shellac and one coat of poly-urethane will make it look the best it can. Matte poly will be the lowest sheen.
The old finish has oxidized over time, so it is not resistant to daily wear.

Thank you so much for your help. I will give it a try! Crossing my fingers that all will look well. With having two children under 3, completely re finishing the floor isn't an option. But the floor looks so bad in areas I just can't handle looking at it anymore. So off to the store for shellac and matte poly I go! I wasnt sure if the matte poly would have been "too dull" looking when I did my closets, but obviously it is the way to go with my old old floors. Having your insight is much appreciated!