In Mahayana Buddhist philosophy these three words are connected. But in order to understand what this means, one has to know their individual meanings first.
Samsara is the classical Buddhist insight that nothing in this world can bring us lasting happiness. Sorrow, stress, apathy – they are part of our existence as human beings and their opposites don’t solve the human problem. The classic Mahayana image of this is that of a burning house. We live in it. We don’t realize that: we aren’t mature enough. This situation of combined danger and ignorance is what Buddhism points out and claims to have a solution to.
Nirvana is the state of freedom from all that. It’s current in both Mahayana and Theravada Buddhism. It probably goes back to the Buddha himself. Since Buddha turned from that state into a teacher of the world as he knew it, it’s not fair to describe Nirvana as indifference.
Sunyata is a term which literally means emptiness. What it refers to (I’m summarizing beyond what the experts are likely to agree with) is the emptiness of every phenomenon we know of staying power. Nothing is permanent. Nothing is as we think of it. None of our concepts of reality fit reality as well as we habitually think they do. (for those interested: here’s a whole bunch of articles about Buddhist philosophy focussing mainly on Sunyata or emptiness)
Now ultimately Nirvana and Samsara are Sunyata, according to Nagarjuna the main philosopher of this doctrine. John Hick explains it like this (again my paraphrase): The difference between nirvana and samsara is not in the way things are (because life is sunyata or empty), but in the way things are experienced.