Arthur Miller's style in Death of a Salesman can be linked to what he wrote about...
On the whole, his works are about an individual’s struggle with an oftentimes indifferent, harsh, or irrational society...
An author's style will often reflect his tone, and as Miller wrote about the "individual's struggle," we can infer that his style makes use of language that demonstrates the struggles between the characters. Words like "terse," "abrupt" and "argumentative" come to mind.
Style is defined as...
...the writer’s choice of words, figures of speech, devices,...
It deals with "expression in writing and speaking."
The use of this kind of language can be seen between Willy Loman and his son Biff. Willy and Biff interact very different than Willy and Linda: but the style is the same. Willy picks at Biff, while he dismisses Linda. There is a great deal of frustration, poor communication and resentment between the characters. Biff is torn between wanting to live up to his father's expectations and wanting to make a place for himself in a world he chooses.
In one scene, words like "nuthouse" and "crazy" are used, and an undercurrent of dissatisfaction, embarrassment and resentment run through the discussion:
I don't care what they think! They've laughed at Dad for years, and you know why? Because we don't belong in this nuthouse of a city! Why we should be mixing cement on some open plain, or—or carpenters. A carpenter is allowed to whistle.
Biff is struggling to find happiness and self-fulfillment. But Willy wants Biff to be what Willy wants and finds fault with Biff's ideas. As much as Willy criticizes him, perhaps Biff is more realistic than everyone else: maybe he could achieve the "American Dream" with some family support.
Miller's dialogue illuminates the characters' interactions: exemplifying their weaknesses and their unhappiness. Linda is always pleading for peace. Hap is acts content, but keeps his head low because he has actually done nothing with his life. Biff is desperate to please his father, but struggles to find personal satisfaction. And Willy's fragile mental state is exposed as he moves between being the adoring younger brother (as he talks to a figment of his mind—his dead brother Ben), Biff's disgusted father, a dismissive husband, and a salesman always looking for the big score.
To Linda, he says things like, "I heard what he said!", "Will you stop?", "Stop interrupting!", and "What's the matter with you, you crazy?"
Ben was/is Willy's hero because he was financially successful. Ben is not the great man Willy imagines him to be—he advises a younger Biff:
Never fight fair with a stranger, boy. You'll never get out of the jungle that way.
Because Willy has always tried to emulate Ben—he is never happy with himself. His brother "tells" Willy to leave what he has: go to Africa or Alaska. Ben has planted the idea in Willy that his life isn't good enough. Because of this, Willy is a man of wild—and unrealistic—ideas.
By the end, the anxiety that permeates the family drives it apart. Miller's style creates the tone—which leaves the reader with the feeling that the American Dream is not for everyone. Biff wants it but can't be "his father's man." Willy thinks it's there for the taking—you can talk your way into it. This is a story of broken dreams and desperation. Miller's style of writing convinces the reader that for some, the American Dream is just that—a dream.