How did Elinor deal with the situation which they were asked to leave Norland by John Dashwood ?

I'm not sure what you mean. The women were well aware they'd have to Northland after their father's death, as the home would go to their half brother. They women have no money, and John, although he wishes to help them in the way he promisede his father is pressured by his wife to do as little as possible.

Elinor, of course deals with everything in a sensible manner, thus the name of the novel. She is the one who watches the money, accepts the offer of the cottage, and keeps everyone together.