Short and Simple, but Sometimes Surreal
Overall, the writing style is pretty straightforward. O'Neill was a twentieth-century American playwright, and the play reads like it was written by a twentieth-century American playwright. Still, it's important to remember that O'Neill is trying to capture both a specific historical time period, as well as some class differences, so the prim and proper speech of Lavinia—who just can't bring herself to call her mother a whore no matter how much she wants to—is going to sound a lot different than Seth's more working-class way of talking.
And, every once in a while, especially when a character has gone slightly off their rocker (okay, okay—it's usually Orin), they can let loose with some things that don't make sense on the first read-through. Take the conversation that Ezra tries to have with Christine before she poisons him. He tells her,
This house is not my house. This is not my room nor my bed. They are empty—waiting for someone to move in. And you are not my wife! (Homecoming, Act 4)
Super dramatic and intense, but all he's really saying is that he knows she's not in love with him and he's suspicious of her. But O'Neill has him say that in an emotionally heightened way to add to the strangeness of the whole atmosphere.
Orin has his share of bizarre and vague dialogue, as his memories of the past get mixed up with the present, and his mental state goes downhill. It's almost like he's reacting to something other than what's in front of him. At these times, the reader has to work hard to figure out what's up. Our confusion is meant to mirror his.