From Storm in Heaven:
During the final years of the Taisho Era (circa 1926), the gloomy tea house Ginseikan had a very special patron. Hiruko is a Baku, a being who eats nightmares. Customers come to the tea house every night seeking release from the suffering in their nightmares, and for the price of the tasty nightmare, Hiruko will walk their twisted dreams with them.

Note: Yumekui Kenbun ran in the shoujo magazine Stencil up until the 3rd volume and then got moved to the shounen magazine GFantasy.

Mikage has just arrived at a new school. But why can't he remember anything about his life before the moment he set foot in the school grounds? His classmates, while appearing ordinary enough, all possess strange habits and weird personalities.

Soon after, our bewildered protagonist is summoned by one of his teachers, who claims that Mikage has the power to influence a 'parallel universe' - and that his interactions with his classmates will decide the fates of the inhabitants of that universe. Though initially fascinated, he soon finds out that these 'powers' do not bode well for his new school life...