Lionel Shriver is a virtuoso at describing what it is to be uncomfortable in one’s own skin. It is only the young, in this phenomenal collection of short stories, who are thoughtlessly content. But their self-involvement (in Domestic Terrorism and Kilifi Creek) is shown to be outrageous, and entertaining too – up to a point. Liana is a vivacious, free-loading young woman who never asks herself whether she is taking liberties when she invites herself to stay with an elderly couple in Kenya. “Although Liana imagined herself undemanding, even the easy to please required fresh sheets, which would have to be laundered after her departure.” Liana persists in feeling that her vitality is doing her hosts a favour, unaware how tired the obligation to socialise makes them.

Liam is a maddening young man (in a story that will alarm and amuse every parent saddled with grownup children at home) whose girlfriend defends his slothful existence to his mother: “This whole idea of ‘doing something’ with your life, it’s wrong-headed. Ask Liam – you maybe don’t realise, but your son, he’s into some profound shit. You are your life. It’s not outside you. You can’t ‘do something with it’ like a toaster on a table.” While Liam pursues the sensation of being himself, his parents do stuff – they put the toast on the table: he brings in no bread at all. And then they decide they’ve had enough. Shriver does not crack a smile – her deadpan quality is her forte – but she makes sure you do.

The novellas and stories often seem to be in communication with one another in an unusual and pleasing way. She writes especially well about how the places in which we live affect us and sometimes shackle us. Our houses are a second skin, our carapace. A flat in Belfast (The Subletter) is a rum character: “The posture of the house on the hill was drawn up, bosom high, like a turn-of-the-century dowager a few too many cream teas on.” A jerry-built house in New York (Vermin) is free and easy – until the couple renting it buy it. The opening line is: “I don’t know if the moral of this story is that you should never buy a house.” A beautiful Georgian house (Negative Equity) with “slate flooring” and “funky lines of mismatched spice” refuses to extend its perfection to the people who occupy it.

This is a collection about ownership in the larger sense, about how we do – and do not – possess ourselves. Sometimes, other people move in on us like squatters. Family can claim us too (there are two discomfiting stories about father-son relationships). The opening novella, The Standing Chandelier, is the collection’s not-to-be-missed highlight. It explores the idea that, given the will and words, any personality might be rewritten: “you could probably savage the personality of everyone on the planet if you wanted to”. (Shriver certainly could.)

Jillian Frisk is an extrovert artist who, when people take against her, tends to take their views to heart. She has a best friend in her male tennis partner and ex-lover, Baba – but Paige, his wife-to-be, emerges as a bad fairy, determined to end their friendship. This is a story that turns on its own axis. One’s sympathies are with Jillian, yet Shriver insists that one also understand Paige’s reasons for finding her beyond the pale. The story proceeds with assured unpredictability and you recognise – fuming all the way – the artistic rightness of each development.

When it comes to what Thomas Hardy called “life’s little ironies”, Shriver is ahead of the game. Her stories are filled with irony and psychological shafts of light. She understands the oddity of what it is to possess: “It is funny how you can covet what you have.” With most short story collections, it is an effort to keep restarting the narrative engine with each new story. But Shriver has the gift for making one instantly curious, entertained, involved and ready to move in – no matter what the property.

• Property by Lionel Shriver is published by Borough Press (£14.99). To order a copy for £11.99 go to guardianbookshop.com or call 0330 333 6846. Free UK p&p over £10, online orders only. Phone orders min p&p of £1.99