I recently had a sick hen so I bought "The Chicken Health Handbook". by Gail Damerow. It covers just about every disease a chicken can get. The only one that mentions "a penguin-like posture" among it's symptoms is Colibacillosis (aka E. coli infection). Which would fit because in her other book "Storey's Guide to Raising Chickens" she says that Enteric Diseases such as E. coli (among others) are characterized by loose droppings, weakness, increased thirst, dehydration, and weight loss.
The Health Handbook lists some of the other symptoms as- a clear eye that becomes blind, swollen leg joint filled with golden-colored fluid (could that be why she's walking strangely?), yellow, watery, or foamy diarrhea, cessation of laying, upright penguin-like posture.
Cause- many strains of the bacteria commonly found in the poultry environment often infect birds with impaired resistance: often occurs as a secondary infection.
Transmission- is through infected droppings, so if you think this might be what she has I would keep her isolated and try to do some clean-up as much as possible where you keep the rest of your flock. I would also watch them closely to see if any of them are showing any signs of illness.
Unfortunately the book does not go into great detail about any particular disease, as far as treatment goes, and it's fairly vague as far outcome is concerned. She does say to keep birds warm and supplied with a high protein ration; also that Vitamin E supplement is recommended and it can be treated with antibiotics if caught early. However, she doesn't specify what "early" is. But if it's only been a couple of days, you might be ok.
She does go into what the postmortem findings would be, which I won't give you the details but I think it explains why her stomach is distended.
If you think that this sounds like what she has I would consult a vet, for treatment options, outcomes, recovery (like will she ever lay eggs again?), etc. as the book is fairly vague on these points.
I hope that helps a little. Good Luck!
