Greetings, I am Dr. Pat. I have worked with birds exclusively for many years.
You are correct to be worried about diet.The goose is at the right age where nutritional issues can start showing up. And one of them is reduced immune system. There are dozens of possible bacterial, fungal, viral and parasitic infections that could be affecting him.
mazuri.com is a good place to start on age/flock/species special diets.
Ideally, he would be on age-appropriate, goose-specific pellets with greens and pasture. At minimum he should be on waterfowl crumbles or the mixed flock diet you have. In a flock situation it is difficult, both because he takes his cues from the chickens and because he has personal preference for the other diet. It is a difficult problem and you may have to separate him for a month just to work on his diet.
The voice is very concerning. The "voice box" in birds is deep in the chest, and any change in vocalizations indicate pneumonia, airway blockage or inflammation in the deep airways and/or lungs. There are dozens of possible bacterial, fungal, viral and parasitic infections possible.
What is your geographic location and local weather?
Can you tell me more about the bird?
How long has this been going on?
How long have you had him?
Where is he from?
Any accidents or trauma?
Interactions with other birds/pets/children/guests?
What is the usual diet? has it changed recently?
What is the water source(s)?
Has the bird gotten into anything?
These signs are of a very sick bird, and not specific to any one disease. And that means it is not fair to you or the bird to guess, there are so many possibilities.You are going to need local help on this, and a scientific and solid diagnosis to find safe and effective treatment.
The challenge is to find out exactly what is going on, since treatment will depend on careful and accurate diagnosis.
You can examine the bird thoroughly again, including opening the mouth and having a good look in there for mucus, redness, masses or anything else unusual. You can take the temperature gently with a rectal thermometer. Anything above 105F/40C is significant. Palpate the tummy for an egg, fluid, lumps or anything else. Check all the joints for swelling, pain, and mobility.
Move the bird indoors to an aquarium, box or carrier with soft towels or hay in the bottom, no perch, and food and water in low bowls that can be reached easily. Keep her partially covered, warm and quiet.
The bird, bowls and unit must be kept very clean.
Do not try to force food or water. You can offer warm cooked rice, pancakes, cornbread, grapes, melon, greens in addition to normal food.
I know it is expensive, but you may not have many home options, because the first thing you need a vet for is to find out what is going on. Treatment is only as good as the diagnosis. If you call around, you may find a vet to work within your means.
She needs to see an avian/poultry-experienced veterinarian ASAP for complete examination, diagnosis and appropriate treatment. Check
https://aav.site-ym.com/?page=basiccare click on "find a vet"
for members of AAV in your area.
The expense for this is going to be a lot less than inefficient, ineffective, dangerous treatments, guesswork, and loss of the flock; not to mention possible implications to human consumption of tainted eggs. Many states/governments have poultry diagnostic labs that charge very reasonable fees to test for common diseases.
Because you have others and presumably use the eggs, it is important to have a solid diagnosis and treatment safe for egg consumption. You can check with local County Extension offices, the closest Ag university with a poultry department, or with the closest vet school for a local referral.
If this were my patient, I would start with complete fecal analysis and direct smear, stained with Sedi-stain and unstained for multiple parasites, fungi, spirals; direct smear stained with Sedi-stain and unstained of the oral cavity; bacterial culture and sensitivity of the feces and choana. Depending on the case I might do a fungal culture. Routine blood work is necessary to rule out other issues. There are MANY DNA/RNA tests for bird diseases. Ultrasound is often more informative than radiographs and does not require anesthesia (ask your vet about this option). Generally I start them out on medications as indicated by the tests.
Pet/feed store medications and home remedies are harmful, ineffective, immuno-suppressive, and make them much worse and may interfere with the veterinarian's diagnosis and treatment. Do not use them.
Check for fly and mosquito access, as they can carry certain diseases, and check for external parasites. Mites, lice and fleas (in some areas, ticks) can contribute to over-all health issues, anemia, and disease transmission.
She may need injectable antibiotics, calcium and many other medications. Act quickly and good luck.