In Hamlet, what characters are emotionally poisoned and where/how does it occur?
If we consider that being emotionally poisoned causes a character to behave contrary to the way they normally would or to act in a way that reflects a noticeable change in character, then we can start with Hamlet himself.
Hamlet is dejected at the beginning of the play. His emotions and his behavior changed when his father was murdered and his mother married Claudius quickly thereafter. So, Hamlet was changed before the play begins. We know this because Claudius and others comment on Hamlet's moody and, later, his mad disposition. Hamlet is just as upset at his mother's quick marriage as he is of his father's death:
O most wicked speed, to post
With such dexterity to incestuous sheets!
It is not, nor it cannot come to good. (I.ii.156-58)
As the play continues, Hamlet's moodiness becomes madness and his behavior particularly affects Ophelia. This madness is all part of his "method"/plan for revenge but his disapproval of his mother's quick marriage to Claudius has made him (Hamlet) despise women in general. Ophelia did not expect this change in Hamlet, and she too became emotionally poisoned as a result of it. Hamlet takes out his angst and madness on Ophelia in Act 3, Scene 1 when he tells her to get to a nunnery:
Get thee to a nunnery, go, farewell. Or if thou wilt needs marry, marry a fool; for wise men know well enough what monsters you make of them. (III.i.137-39)
Hamlet continues to treat Ophelia poorly, her behavior changes, and she eventually kills herself.
Hamlet's behavior also affects Claudius. One could argue that Claudius was "emotionally poisoned" before the play starts because he is ethically poisoned as a result of his deed (killing the king and taking the king's wife). But within the context of the play, Claudius' character does not change. He reacts to changing circumstances with the same coldness that led him to kill the king. Claudius does become more and more concerned with Hamlet as a rival. That being said, Claudius does not really stray from his conniving ways. But as the play goes on, Claudius does become more and more serious about getting rid of or killing Hamlet. In Act 4, Scene 7, Claudius conspires with Laertes to have Hamlet killed.
Gertrude is an interesting character in that she does not really change. She becomes increasingly concerned about Hamlet, certainly after she discovers that he killed Polonius (Act 3, Scene 4). Gertrude never changes her essential character but she is very emotionally affected by this:
O Hamlet, speak no more!
Thou turn'st mine eyes into my very soul,
And there I see such black and grained spots
As will not leave their tinct. (III.iv.78-81)
Among the remaining characters, Laertes does not change. He is known for being brave and quick to act or fight. He immediately accepts Claudius' invitation to avenge his father (Polonius). Therefore, Laertes continues to express his desire for action. Polonius also does not change in terms of his character/behavior. Rosencrantz and Guildenstern are also fairly static (unchanging) as well even though they are characterized as being easily manipulated.
Since we don't know how or why Claudius decided to murder his brother, we can't really say that there was a defining moment in which he was emotionally poisoned and became capable of murder. Hamlet and Ophelia are the characters who are most emotionally poisoned, in terms of whose behaviors change most dramatically. Hamlet's change in behavior plays a big role in Ophelia's change in behavior. Consider this: Hamlet's emotional poison leads him to construct a dramatic, complicated plot to avenge his father. Ophelia's emotional poison eventually leads to her suicide. These two characters exhibit the most dramatic changes in behavior and action.
Ophelia is one of the most emotionally poisoned characters within the play. Hamlet's change in character confuses Ophelia as to what he feels and this also cause her to deal with verbal and mental abuse. Hamlet calls Ophelia horrible things once he is aware that someone is spying on them. On top of that, Hamlet manhandles her when he is talking to her and no one butts in to stop him.