In Death of a Salesman, how does the Loman family handle their problems?

The Lomans, individually and as a family, are very ineffective in dealing with their problems. Linda tries to solve family problems by trying to control the others' behavior. She attempts to protect Willy's health and safety, as well as his ego, by hovering over him and making excuses for him. She tries to solve the problems between Willy and his sons by begging Biff and Happy to treat their father with more respect and by trying to convince them that Willy is a good man. Linda frequently runs interference between her husband and her sons. 

Happy deals with problems by refusing to acknowledge them or by making wild promises that are forgotten as soon as he makes them. 

For most of his life, Biff dealt with problems by lying, stealing, or simply running away. After coming home for the last time before his father's death, however, Biff tries to have an honest discussion with his father, but gives up in the face of Willy's anger and denial. Biff faces the truth about his family when he tells Willy, "We never told the truth for ten minutes in this house!" 

Willy deals with some problems by voicing them to Linda (concerns about his job), but his deepest and most significant problems he buries for years, until the end of his life when they finally overwhelm him. Willy tries to cope (with more denial), but he is finally destroyed by his angry outbursts and suicidal depression.

In "Death of a Salesman", what are the strengths and weaknesses of the Loman family?

Let us start off by thinking of the strengths of the Loman family. In one word, I would say the most significant strength can be summed up in the figure of Linda. She is the driving force of the family that tries to bring her sons and her husband together, and also tries to keep her husband on the straight and narrow, caring for him and looking after him. She is such a force of goodness as she is always optimistically encouraging him in spite of his obvious failings and his increasing lack of ability in sales.

Thinking about weaknesses, there are a number we could comment on! One of the biggest however is Willy and his obvious slide into dementia as he finds his own reality of life far easier to cope with than the real reality that threatens to expose all of his illusions and pretensions. Not only does this threaten the stability of the family economically, but as the play develops it becomes clear that his focus on the American Dream and his unerring belief in its supremacy has influenced his children to grow up having unrealistic expectations of themselves and their lives. This is one of the central conflicts of the play and is something that threatens the very fabric of the Loman family.