Steven Millhauser is a master of the weird, the eerie, and the suburban strange. He has many stories online in the New Yorker (you can read several stories a month before you need a subscription) but his story ‘Cathay’ is also online at Electric Literature.
Kij Johnson has an enviable imagination. Her collection, At the Mouth of the River of Bees, is a must-read, but rarely mentioned in the UK. She has put several of her stories on her website. Favourites of mine on this list are ‘Spar’ and ‘26 Monkeys, also the abyss’.
Aimee Bender ranges from the bizarre to the brutal in her fantastical scenarios. I highly recommend the story collections listed on her website here, but scroll to the bottom of the page for links to stories of hers online, including the great ‘Americca’.
George Saunders specialises in memorable voices and extrapolations into the fantastical that critique modern American culture. Read all his collections! You can find many stories of his on the New Yorker, but ‘Sea Oak’ is free to read at the Barcelona Review and is hilariously horrible.
Helen Oyeyemi has created her own domain of the strange and wonderful, in both her novels and short stories. You can read ‘Books and Roses’, from her latest collection What is Not Yours is Not Yours, online. I also love her story/novel hybrid, Mr Fox.
Kirsty Logan shares many of her fantastical short stories on her website (scroll down the page). Amongst these, ‘The Gracekeeper’ is notable for its atmosphere, world-building and language-play. This story also became Logan’s novel The Gracekeepers.
Lucy Wood’s collections, Diving Belles and The Sing of the Shore, blend Cornish folklore with some of the harsher realities of life in that stretch of the country. She can be funny, frightening, sweet and uncanny. You can listen to her story ‘Of Mothers and little People’ online at The Story Player.
Kelly Link plays by no rules in her often-long short stories, and they are all the more transporting and memorable for it. There are many links to her short stories online on her website (I particularly like ‘The Faery Handbag’), and her brilliant ‘Catskin’ is at Lightspeed Magazine.
Claire Dean’s short stories sometimes draw on fairy-tale and legend, but she also does melancholic uncanny and weird very well indeed. You can find links to many of her stories on her website (scroll down) – I love them all but recommend ‘Feather Girls’ and ‘Chorden-under-Water’ especially.
There are so many more I could mention, but I this free online selection should keep you going for a while. If you discover an author you love, do buy their book – what’s online is just the tip of a richly weird iceberg of fantastic literature.