The Halloween black cat standing sideways -- her coat bristling, her back arched, her tail frizzed, her eyes dilated and her face in a hideous grin -- is not in a state of demonic possession, nor is she the embodiment of evil. She's just scared out of her feline mind.
The physical process that changes a cat's coat from sleek to furball is called piloerection. The word literally means "hair upright," and that's what happens. As a result of a stress-related hormone cascade, tiny muscles in the skin at the base of each hair contract, lifting the hair away from the skin.
Piloerection happens to many animals, including humans. Other technical/scientific/medical names for it are horripilation and cutis anserina (goose skin). When it happens to people, we call it gooseflesh or goose bumps, because it makes our almost hairless skin look and feel bumpy, like the skin of a goose (or a duck or a chicken) with all the feathers pulled out.
Piloerection tells you that a cat is under stress, but not what kind of stress. When Fluffy makes a big tail, it can be for many reasons. If she's being attacked (or thinks she is), she needs to look bigger and scarier to make her enemy think twice about moving in. So she puffs up, turns sideways and arches her back .
If she's cold, piloerection traps air in her coat, and the dead air acts as insulation to hold in body heat. If she's sick, that's stressful, too. She could even be having a flashback to some kittenhood mental or emotional trauma.
Once a cat is in a stressed state, it can take some time for her to calm down completely. She might hiss, spit, scratch, bite, have dilated pupils, puff up again (or stay that way), or otherwise behave abnormally for hours or even days. It's a matter of the hormone overload -- a sort of feline PTSD -- wearing off.
Be careful how you handle her and even how you approach her, as you could unintentionally set her off again. Unless she's injured, give her time to be alone or hide if she needs to, and she'll eventually be her old sweet self again.
If she's bleeding or hurt from a fight, do your best to get her into a carrier, and take her to the vet as soon as possible. If she's hiding, drooling and not eating or drinking, ditto -- but very carefully. If you must handle her, wear heavy gloves to keep her from hurting you out of pain or panic.