The three American female writers under discussion here are all creators of fiercely original fiction, owners of voices that are outsize in their idiosyncrasy and ambition. Elizabeth McCracken is perhaps the most conventional of the three, though no less daring or unflinching. The calm, terrifying stories in “Thunderstruck” (Dial Press, $26) all center on loss or disaster. In McCracken’s universe, children suffer illness, abandonment, neglect and other terrible crimes. (If you’re a helicopter parent with an active imagination, this book is not for you.)

This is fiction about “mapping the unmappable,” the emptiness of contemporary life, the frightening lacunae in the web of society. How easy it is to disappear. McCracken’s prose sails along crisply until it strikes, sickeningly and thrillingly: “They found a body.” “We heard the big news slowly.” “This was why you had two children.” These stories have the jittery emotional valence of fairy tales, where to name dangers — the wicked witch, the hungry wolf — is somehow to subdue them. The result is like some set of forgotten Brothers Grimm tales translated into the jolting anomie of modern life. “They had some terrible story, too, or soon would,” the narrator of one particularly disheveled story says, of a feckless young couple. “He wished he found this realization ennobling, but he didn’t: he was furious at them for . . . whatever tragedy was just a headlight glow on the road ahead.”

To read Rivka Galchen is to enter a wonderland where the bizarre and the mundane march in unlikely lockstep. I have spent a good part of the week like some word-mechanic looking under the hood of an exotic car, trying to figure out what makes the odd little fables in “American Innovations” tick (Farrar, Straus and Giroux, $26). Part of it has to do with the way Galchen emphasizes the unexpected, like a magician who directs your attention one way while the real action takes place elsewhere. “The Entire Northern Side Was Covered With Fire,” for example, opens with a woman finding that her husband has just left her and her unborn child, taking with him “a particularly nice Parmesan grater” but leaving behind his winter coat. The woman’s first reaction, naturally, is to “search online for a replacement . . . because I had really liked that Parmesan grater.”

Faced with utterly bewildering circumstances — ghosts, time travel, possessed possessions — Galchen’s characters respond with a literal-minded matter-of-factness that’s funny and heartbreaking. They speak of “the awful sense of wanting some other life,” of how “our world obeys rules still alien to our imaginations.” It’s their sense of being not quite at home in the world that sticks with the reader, who is left feeling oddly exhilarated after these disjointed adventures.

Lydia Davis, meanwhile, continues to expand her inimitable oeuvre with “Can’t and Won’t ” (Farrar, Straus and Giroux, $26). It assembles more than 100 of her stories, one-liners, anecdotes, dreams, vignettes and shaggy-dog tales, along with a number of passages she has translated from the letters of Gustave Flaubert, which seem strangely of a piece with the rest of this collection. Davis’s voice, as readers of her monumental 2009 “Collected Stories” know, is immediately identifiable and utterly sui generis: Her short works range from a sentence to a few paragraphs and generally present some cryptic statement in a glancing, artlessly conversational style. Here’s “Her Geography: Alabama” in its entirety: “She thinks, for a moment, that Alabama is a city in Georgia: it is called Alabama, Georgia.” Davis’s pieces are a species of conceptual art, akin to the work of Barbara Kruger and Jenny Holzer, her contemporaries and peers in the downtown art world of the 1970s. A masterful piece like “The Cows” plays with the shifting nature of perception, time and distance through a sequence of precise, explicitly visual observations. And from one of the last stories in the book, this pitch-perfect koan: “Life is too serious for me to go on writing. . . . There are other things I should be doing instead.”

Lindgren is a writer and musician who lives in Manhattan.