Hi.
I'm not sure if internal laying will show up in an x-ray. It is usually just the egg yolks, released from the ovary that get deposited in the abdominal cavity, so they may not be apparent on an x-ray.
The common causes of abdominal swelling.... which usually leads to soiled or lost feathers below the vent, runny poop and penguin stance are:-
1. Internal laying..... which can lead to ascites (water belly) and/or Egg Yolk Peritonitis
2. Ascites caused by some other means.... liver, kidney or heart disease/failure.
3. Salpingitis..... where an infection in the oviduct causes egg matter to build up and solidify.
4. Tumour.
Internal laying with associated ascites is probably the most common. Yolks fail to travel into the oviduct when they are released from the ovary and drop into the abdominal cavity each day, where they build up. The pressure of them over time causes fluid to leach out and sit in the bottom of the belly swelling whilst the squashed, solidified yolks float above impinging on the flow of waste through the digestive tract and also putting pressure on the heart and lungs. Hens will usually look healthy, with red combs as they continue to ovulate, but eventually they start to struggle to walk and breath as the mass becomes too large and the digestive tract backs up as only fluid can pass through the areas that are restricted by the masses of yolks. The hen will probably feel quite heavy due to the mass of yolks and fluid but start to lose condition (breast muscle will waste) and may also experience crop issues as the digestive tract slows down.
Salpingitis will cause similar digestive impaction, but usually there will be no associated ascites.
Unfortunately most of these issues will become fatal and are not reversible unless caught early enough. Hormone implants are being successfully used by some people to prevent internal laying from progressing but are expensive and need to be repeated every 3-6 months. Salpingitis may respond to antibiotics if it is caught early enough but usually it has progressed too far and removing the large mass of infected eggs (lash eggs) is impractical.
Ascites can be drained with almost immediate relief but unless the overriding problem causing it is addressed, it will reoccur, so only a temporary solution, which might buy the hen a few more weeks or months if repeated.
Tumours will be terminal, especially if they are large enough to cause a penguin stance/walk.
Unfortunately a penguin stance is likely to be an indication that things have gone too far and unless you are prepared to fork out hundreds of £/$ every few months, you might be best to euthanize without incurring more vets fees.
The best way to improve your knowledge of the problem is to do post mortem examinations of the birds (necropsies) to find the cause in each case. I know this is not for everyone, especially when it is a beloved pet, but sometimes there are things to be learned like dietary changes that can be made to prevent others suffering the same fate..... eg. excess carbohydrate from scratch can cause fatty deposits around the organs which can lead to fatty liver, internal laying and heart problems.
I'm sorry I can't offer more hope for your girl. If it was internal laying and you had "the cash to splash" hormone implants would be the way to go and/or draining of fluid in the case of ascites.
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