Write an essay on how O'Flaherty uses language to communicate his theme in "The Sniper"? (Include quotes.)

This is a really solid essay topic, and the link it proposes between the author's language and the theme is a link that I think can be defended. I can offer advice and hopefully give you and the essay some direction.
I would approach this essay topic from one of two directions. Either analyze the language used and pull a theme from that, or analyze some themes and figure out how the language used highlights them. I would go with the second option because it allows you to think and start with an initially bigger picture and use specific lines from the story to highlight the theme that you have chosen.
Despite being such a short story, "The Sniper" is full of possible themes to explore. There's obviously a theme about warfare, and more specifically the theme is about civil warfare. There's another theme about perseverance and ingenuity, and that is illustrated by how the sniper kills the other sniper despite being wounded and essentially pinned down. For this essay, I would pick a theme that focuses on a specific part of war. I would focus on the theme of dehumanization. War dehumanizes people on all sides of the conflict, and I think this theme can be well explored through the language that the author uses in this story.
One key to the language in this story is the fact that no character is named. The characters are described, but they are not named with proper nouns. The story has this sniper, that sniper, an old woman, and so on. This lack of naming the characters keeps the characters distant from readers. They are essentially interchangeable parts. There is likely going to be another old woman or soldier for the sniper to shoot at. We, as readers, have no real connection with these people. They are essentially things.

Then round the corner of a side street came an old woman, her head covered by a tattered shawl. She began to talk to the man in the turret of the car. She was pointing to the roof where the sniper lay. An informer.

The sniper has been at his job for awhile. He's used to killing people, and he no longer questions the morality of it. He's used to seeing death.

His face was the face of a student, thin and ascetic, but his eyes had the cold gleam of the fanatic. They were deep and thoughtful, the eyes of a man who is used to looking at death.

The sniper doesn't question the morality of killing the old woman or the man, because at this point, they aren't people to him anymore. They are targets of equal opportunity. It doesn't matter whether the target is man, woman, young, or old. The sniper doesn't care. He has been so desensitized by the war that he no longer sees them as people. The war has dehumanized those people into mere targets. Notice that the sniper disregards the information about the woman being a woman, old, and tattered looking. None of it matters. She is an informer, and the author doesn't even write it as a complete sentence. It's two words: "An informer." That's all it takes for the sniper to know that particular target needs to be hit. The simple, direct, and objective terminology that the author uses to describe people is effective at removing their humanity.

The woman’s corpse lay still in the gutter.

The above sentence is cold and to the point. There is no remorse in the statement. She, like the other man and the opposing sniper, need to be eliminated. The sniper doesn't need to feel bad, because it is kill or be killed, and they aren't really people in his eyes anyway. They are informants, targets, and/or enemies.