I would advise the tower controller where on the runway the bird strike occurred. If the birds were sitting on the runway, the tower controller would likely have someone go out and inspect the runway. This would probably close the runway until the inspection was complete. The tower controller would then pass that information along to the next landing aircraft. He could give that next aircraft the option to land on the parallel runway (assuming there was still time for that flight to sidestep over to that parallel runway) or have him go around.