How do the violent episodes in Of Mice and Men present Lennie's character to the reader?
Refer to the series of events in which he killed the mice, then Curley's wife, as well as the girl in weed and the fight with Curley.
Lennie is a classic example of someone who both doesn't know his own strength and can't control his emotions. When he gets angry or scared, the reaction is always the same. He only comes to the realization that he was wrong after the fact, after the violence has happened, and then he regrets it loudly and openly.
Even though he is violent, Lennie is still presented as a sympathetic character. He is likable and funny, even though he doesn't know it. The reader knows the things he does are really bad, and cannot go on without Lennie getting locked up or killed, but in the end we still want him to get away.
The girl in Weed is sort of a vague stroy about a girl in a red dress. George explains it to Slim later in the story, but we don't get a lot of details. With Curley, George told Lennie to fight back, and he did, spectacularly, but feels very badly after he hurts Curley, unsure when violence is OK since George told him to. Curley's wife's death was accidental, like the killing of the mice (by "petting them too hard"), again, Lennie not knowing his own strength.