How much color have you sanded off. Since you are refinishing, if you haven't sanded the wood down to the natural color they should stain much the same. Normally the old stain will seal the wood like a wood conditioner. If you have sanded the wood down to the natural color then I would experiment with using a wood conditioner on the pine. It will take some tinkering to tell how much to thin the wood conditioner to make the pine match the oak. Since you are working on old wood I would make sample spots on the stairs in places where you can sand it off.