Assuming they are solid boards and aren't warped and buckled then you sould try sanding them, most solid boards can be sanded a couple of times during their lifetime. A drum sander could be used to take off the top layer and leave a nice finish. They do create a lot of dust.
Another option to consider might be a square buff, basically a viberating square sander, easier to use and not as harsh as the drum sander but may gives a very good finish. Once sanded and cleaned apply two or three coats of a two pack varnish.