Off-hand I would think that what you are trying to do might be a little difficult. Generally, red oak is darker and more red/brown than naturally finished pine, even after ageing, which turns the pine more brown and yellow.
Oil based poly will develop an amber/yellow hue so use water based.
Since the wood you have is relatively dark and the wood you want it to look like is relatively light, I would just try to use a very light brown stain.
One last thought...
You really didn't define what the pine you are talking about looks like. I have seen a pretty decent variety in final appearance of "pine" floors. Much of how they end up looking has to do with the stain and the hardcoat finish choices, but other factors can be important too, such as the exact species of pine you are talking about, its age and the kind of exposure to sunlight it might have received over time. So... when you say "look like pine" we don't really know what you mean with any certainty. Pine floors can be light tan colored with yellow hues, or they can be light brown, or they can be reddish. I would get a bunch of your oak scraps and a bunch of those small minwax stain cans and start experimenting.