Can you show pictures of the floor?

If it's moving underfoot, something is wrong - maybe rot or just old, brittle flooring.

Sounds like installing new, or sistering the old, floor joists is in order. And replacing the old flooring.

Moving underfoot might mean different things to different people. Do you feel floor bounce with each step when someone is walking 6 feet away? Or do you feel random boards give as if they were resting on foam rubber? You are lucky in some ways,easy access from underneath, imperfect match can look ok on destressed floors.

Look at the underside of the bouncy area of the floor. What does the subfloor look like? Post photos from above and below.

After sanding and refinishing pine floors in my previous home the wood flooring became thin and weak underfoot. While renovating the rooms below I used a hand grinder to cut the nails protruding through and cut plywood to fit in between the joists. I think screwed 2"x3"s into the joists to hold the plywood tight to the bottom of the flooring. Worked great for years.

If your floors are like ours, they have no subfloor underneath them. It is just the wood floor over the joists. If this is the case, you may just need to sister new joists to the old. Ours are 24" on center, which I believe is too far apart for current code. Our have splintering in the areas of most use. I have tried a lots of things to stop the splintering without success. You can replace the individual boards if you can pull them from some other part of the house, like closets. I have not tried this yet. There is info about this on This Old House's site.

http://www.thisoldhouse.com/toh/article/0,,218102,00.html