Thor: Thor sleeps anywhere, and naked. This has caused a few issues.
Steve: on his back or side, straight as he can, barely moving. This is a habit left over from camps and barracks, squashed in with other soldiers, and from before, from the cold bitter new York winters when he was a kid. The cold was dangerous for him, screwed with his lungs, so every night Bucky would come to his place and squeeze into his narrow bed to keep him warm. He was like a furnace. Steve’s elbows and knees were sharp as knives so he made sure to keep extra still so his friend would be comfortable. Bucky’s warmth probably saved his life.
Natasha: Fetal position. Natasha curls up like a cat, all curved limbs and tousled hair, one hand by her face. She looks innocent, almost at peace. This is because her other hand is wrapped around the gun beneath her pillow.
Tony: Sleeps spreadeagle, mouth open, limbs splayed, wherever he collapses. He goes days and days without sleep; he is the wraith in Avengers tower, making coffee and scrambled eggs at 4am and disappearing back to his lab. Steve’s not much for sleep either, and he’s the only one besides Pepper who can gain access to Tony’s workshop, so he often goes downstairs to find Tony passed out on the floor with a wrench clutched in his fist and oil in his hair. If Tony ever wonders why he falls asleep on the workshop floor and wakes up in his bed with his shoes removed, he never mentions it to Steve.
Bruce: sleeps more than any of them. It’s maybe a metabolism thing. Hulking out uses up a lot of energy, so whenever he shrinks back to regular Bruce-size he eats enough for three and then sleeps for at least 16 hours. He sleeps in fetal position like Natasha, but tighter, knees tucked up almost to his chest, his whole body a clenched fist. It looks almost painful. He frowns and mutters to himself, and sometimes he cries out. There is an unspoken agreement amongst the rest of the team that they won’t mention it.
Clint: Sleeps with his eyes open. Sitting up. On the couch, or on top of the fridge, or on the stairs. Basically wherever affords the best position to scare the shit out of Tony at 3 in the morning.