Midnighters trilogy by Scott Westerfeld

When Jessica Day moves to the seemingly sleepy town of Bixby, Oklahoma, she has no inkling that she'll learn the town's supernatural secrets one sleepy night. When she wakes up at exactly midnight, she sees raindrops outside which appear to be frozen - not made of ice, but rather, suspended in mid-air. She cautiously, carefully treads outside and takes in all of the quiet beauty of the night. She thinks it's all a dream . . .

. . . until her new classmates tell her otherwise. Dess, Rex, Melissa, and Jonathan are connected by the time they were born: the stroke of midnight. This is a stroke of luck, for better or for worse, for it permits them to move around the town during the Secret Hour that starts at midnight, when everyone and everything else freezes. Each teenager has a cool ability which is truly unique. Thanks to Scott Westerfeld's creative mind, even those powers you may think are typical of sci-fi stories, such as flying, have a new spin. He also makes math a superpower. Woo hoo! These powers are tested when the group has to fight the Darklings, creepy creatures literally from another time, creatures that can ONLY move around during the Secret Hour. Research, plans, patterns, steel, and thirteen-letter words must be prepared, and sacrifices must be made.

Read the Midnighters trilogy in order:
The Secret Hour
Touching Darkness
Blue Noon