What is Tennessee Williams' literary style?

Williams came to prominence at a crucial time in American culture when the public consciousness was being transformed with regard to sensitive issues such as sexuality. He provided an "opening up" of the acceptable subjects that could be dealt with dramatically, specifically in women's issues and gay themes.

His central characters are usually women who have some form of extreme trauma in their past or have been rejected by men or society at large. This is true of Laura in The Glass Menagerie, Blanche in A Streetcar Named Desire, Maggie in Cat on a Hot Tin Roof, and other somewhat less well-known heroines such as Alma in Summer and Smoke and both leading women characters in Sweet Bird of Youth. At the same time, the previously unmentionable subject of homosexuality appears in Williams's literature repeatedly. The women themselves are not gay, but often the men in their lives have been gay or are attempting to sublimate their gay tendencies, as Blanche's former beau has done and as Brick in Cat on a Hot Tin Roof does. The style of Williams's dialogue is often extravagant and overstretched, but this is what is often responsible for its effectiveness. Both in subject matter and in its manner of presentation, Williams's plays convey a freedom and an almost wildly uninhibited quality in comparison with American drama of the previous decades.

O'Neill, of course, was the preeminent American dramatist of the period before Williams came to prominence in the 1950s. His work deals with themes of sexuality as well, but not with the almost obsessive force Williams would bring to the subject. If I could pick one of his plays that somewhat anticipates Williams, it would be Strange Interlude. The character of Nina is similar in many ways to a Williams protagonist. O'Neill has his characters speak their thoughts aloud in a kind of stream of consciousness. But what differentiates Williams from O'Neill is the less intellectualized focus within Williams's plays. O'Neill has a tendency to be cerebral. In his greatest play, Long Day's Journey into Night, his main characters are intellectuals: a father and his two sons quote poetry to each other and express thoughts about the absurdity of life (but in a realistic context), against a backdrop of a hugely dysfunctional family dynamic in which substance abuse is a destructive force.

In sum we might say that O'Neill is more complex and "deeper" than Williams. However, the latter conveys emotion and meaning more directly and viscerally and was perhaps an even more seminal force in American drama than O'Neill.

Tennessee Williams used a lyrical writing style that incorporated elements of the Southern Gothic style. The Southern Gothic style often involves making archetypes of southern literature such as the chivalrous hero or the beautiful damsel flawed or grotesque in nature.

For example, in The Glass Menagerie and A Streetcar Named Desire, Williams uses the archetype of the southern belle but subverts this archetype by giving the women in his play grotesque or flawed qualities. The mother in The Glass Menagerie, Amanda Wingfield, presents herself as a southern belle and would like her daughter, Laura, to find the perfect husband. However, Amanda's life in no way resembles a fairytale. Her husband has long ago left her, and she lives in straightened circumstances. Her daughter, Laura, is not a charming belle but a mentally unstable, isolated woman who has a limp. Amanda tells her daughter in the first scene, "No, sister, no, sister--you be the lady this time, and I'll be the darky." Amanda incorporates grotesque elements of archetypal southern womanhood, including bigotry and a reliance on outdated notions of womanhood and courtship. Blanche DuBois in A Streetcar Named Desire also features the elements of grotesquerie that subvert the ideal of the southern belle. While she plays the part of the southern belle, it is merely acting. In reality, she is a penniless older woman who tries to disguise her age and whose husband committed suicide because he was gay. 

In addition to employing the Southern Gothic style, Williams uses a lyrical style of writing, particularly in his stage directions. For example, he begins The Glass Menagerie with the following description: "The Wingfield apartment is in the rear of the building, one of those vast hive-like conglomerations of cellular living-units that flower as warty growths..." His lyrical style emphasizes that the plainness of the Wingfield apartment is a far cry from the southern archetype of the gracious plantation-style home. 

Eugene O'Neill's stage directions are also lyrical at times, like those of Williams. However, his dialogue and writing style are far more straightforward than those of Williams, and his characters, while flawed, do not call on southern archetypes. Instead, his works, such as The Emperor Jones and Desire under the Elms, call on Greek tragedies and their emphasis on the role of fate and on the hero's downfall as a result of his or her own tragic flaws. 

Tennessee Williams' style is characterized by theme, theme related metaphor, theme supporting scenario, setting, and poetic language, Williams' predominant theses are the dominance of a get-ahead society over sensitive individuals (e.g., Laura and Tom) and the dominance of ambitious people over the poetic-artist. Williams often illustrated these themes with physical weak or handicapped characters (e.g., Laura) who represented the failure of weak people in the face of Darwinian survival of the fittest.

Williams dramatic scenarios and settings were critical elements to the representation of his theme. To illustrate his themes related to overpowering, he often employed scenarios of repressed, perverse or abnormal sexual desire (e.g., Laura's repressed desire for ___). Williams' settings were unified with his characters and were thus indispensable to fulfillment of his stories (e.g., the "cage" of an apartment in The Glass Menagerie). As stated in Magill Survey of American Literature, Williams had three styles of settings. The first, evident in The Glass Menagerie, is poetic expressionism; the second is theatricality as in the naturalistic A Streetcar Named Desire; the third, as seen in Suddenly Last Summer, is symbolic, like Sebastian's lushly symbolic environment. Which leads to the final comment that Williams' style leaned heavily on poetic language and devices, a dependency that some critics seem as a limiting influence in his plays.

What are the key characteristics of Tennessee Williams' literary style?

The nature of the question is really broad and subjective. This means that you are probably going to get several different takes on this.  I cannot help but feel that the most significant characteristic of Williams' thematic style is the emphasis of those who are marginalized.  Williams really gives voice to the "fringe" or the elements of social orders that are pushed to the side.  Certainly, this comes out from his own background in his experiences with his sister and his own notion of self as being gay in a society that really had much in way of repugnance for such individuals.  Williams' work focuses much on how these individuals function in a rather unforgiving world.  Characters like Laura or Tom, Stella or Blanche, Brick or Maggie help to bring out how Williams' style seemed to be predisposed to individuals that would have or do have a tough time finding a voice in the modern setting.  Williams' style is one where the sad and delicate nature of what it means to be on the outside looking in is evoked.  He does this in a manner that is not didactic.  It is not in a manner that evokes pity.  Rather, he does this in a style that brings out the character's own weakness while making it clear that the social order that maligns such narratives is also faulty, as well.  In this, Williams brings out a state of being where there is pain and suffering all around.