how is iago responsible for each death?
If you remember, it was Iago who framed Desdemona to make it look as though she was having an affair with Cassius. Othello murdered his wife Desdemona because he didn't believe her innocence. As it was Iago who made up the affair, he could be blamed for Desdemona's death for this reason.
Othello was overcome with guilt after realizing that he had murdered his innocent wife. Again, Iago was responsible for developing the story that led to this death.
Emilia stole the handkerchief from Desdemona as Iago requested, which was the "evidence" that Desdemona was having an affair. When she confesses this at the end of the play, it is Iago who murders her, and he is obviously responsible for this death.
Hope that helps!