We put golden oak oil based stain on medium dark birch plywood. I hate the color. How can we take it off to try again with a lighter stain?

If no sealer has been applied you should be able to remove with mineral spirits (paint thinner). Most of the time you can remove dried stain by applying more of the same stain then wiping. Most of the time some remnants of the stain will remain but not enough to affect the color of another stain.
This is assuming that the stain was a stain only, not a stain and sealer combined.