Sand the the wooden boards containing the holes with a piece of 60-grit sandpaper to smooth down the rough edges of the holes and to remove any splinters. Sand down the entire board, not just the holes, since you must re-stain the entire board. You can sand by hand or use a belt sander to speed the process.
Open a can of pre-stained wood putty that is the same color as the wood floor. Insert a putty knife into the can and scoop out 1/2 tsp. Press the putty into one of the holes firmly and then scrape the top of the hole with the blade to remove the excess.
Repeat the process of pressing wood putty into each of the remaining tack strip holes around the entire perimeter of the room.
Wait until the putty is dry and feels hard to the touch. Sand the surface with a fine 200-grit sandpaper until you can no longer feel the nail holes. Wipe off all of the boards using a tack cloth to remove the sanding dust from them.
Open a can of wood stain in the same color that was originally used. Apply it only to the sanded boards using a paint brush and making single, long strokes. Allow the stain to dry completely and then apply a clear polyurethane coat on top of it to seal the stain.