If you lift her head and support her neck can she eat/drink on her own?
You may need to syringe or tube fluids into her, but you'll have to manipulate her neck up a bit to do that.
As for putting down a hen that's in misery, I use the broomstick method (cervical dislocation). Others will...
Poor girl!
She may have suffered injury. It's up to you to determine if she's in pain/misery to the point of putting her down.
Wry Neck is a neurological symptom, some common causes are injury, disease and vitamin deficiency.
Keep her hydrated and eating. I'd give the vitamin therapy...