There are any number of literary elements to choose from in "House Taken Over," but I can outline a few of the major ones here.
Perhaps the simplest is that Cortázar uses a first-person point of view: the story is narrated by someone directly involved, an "I" who tells the story.
The entire story can be considered an allegory for Peronism, or a form of Argentine populism. The narrator and his sister are representatives of the Argentine bourgeois class: they are idle most of the day, with money coming in from land rentals; the narrator reads French novels; there are only two of them but they live in a huge house; they take up more space than they need, in a family home that they did not earn, but rather was passed down to them. And yet their wealth and their space is being taken over by something (allegorically, the populace, the working class), cutting them down to size and leaving them with nothing. The line "Irene never bothered anyone" is critical within this reading of the story: she was minding her own business. She never went out, never contributed to society or the economy—the narrator did those things, and only rarely. The narrator is painting Irene as a victim of the working class's takeover; she loses everything, which is then presumably divided up among those who could not afford it.
On a less political note, Cortázar also uses suspense and foreshadowing to keep the reader on their toes: we never see what it is that is taking over the house; we only know that once they have invaded, there can be no going back. When the narrator first hears them,
The sound came through muted and indistinct....At the same time, or a second later, I heard it at the end of the passage which led from those two rooms toward the door. I hurled myself against the door before it was too late and shut it, leaned on it with the weight of my body; luckily, the key was on our side...
In this scene and the last are the only times we get a sense of urgency on the part of the narrator; he "hurled" himself against the door "before it was too late." The pace is quick here, and the sudden eruption of the existence of this "other" in the house leaves the reader with a suspenseful, ominous sense for the rest of the story. The "other" taking over this part of the house also foreshadows the taking over of the entire house at the end of the story.
The last element I will mention is the motif of collecting or gathering in the story: motes of dust "rise and hang in the air, and settle again a minute later on the pianos and the furniture." The siblings' income from the farms was "piling up"; Irene has hidden stacks of shawls in a drawer; and when the narrator finally flees, he abandons a large stack of money in his bedroom. This could be read (but is not necessarily intended) to be an indication of the wealth amassed by the middle class and the sheer amount of things amassed in capitalist society, despite their relative idleness and lack of need.