I am not 100% sure what his illness is. I would take him to a Vet, immediately for an accurate diagnosis. But, if that is not an option...here are my best guess and to what is ailing him.
# 1 - Canker, even though it is not the season for it. You identify sores in the inside corners of his mouth, and sour smell.
Treatment is Copper Sulfate in water, use
non-metal waterer, 4-7 days. Or, Metronidazole (Flagyl). Follow up with probiotic for poultry, if you use copper sulfate.
Purchase copper sulfate at the feed/farm store,
ASAP!
#2 - Marek's, because of his paralysis. However, the typical pattern is one leg forward and one facing back. There is no cure for Marek's, just treat symptoms, comfort, warmth.
The fact that he is still trying to eat is amazing. Is he actually swallowing the food. You may have to hold him on your lap while he eats and drinks. Then gently massage his crop a bit, to keep his digestive system moving.
He may also have yeast infection, along with his illness. It is common for multiple issues to cause problems at the same time. If there is yeast in the crop, the copper sulfate will take care of this too. Make sure his crop is emptying, each morning the crop should be empty. Even, during the day, if he eats, check his crop each hour to see if the food is going down. Also, monitor his ability to poop normally.
If his digestive system is working, he has a chance for survival!
If you have some oregano oil you could make a crop tonic for him. Here is a simple recipe.
Crop Tonic:
1 tsp. thick yogurt with at least 3 bacteria cultures in it.
1 drop, Oregano Oil
4 drops Coconut Oil, melted or Olive Oil or Grapeseed Oil
4 drops water
Mix in a shot glass, stir well, and administer 1 mL, orally with syringe.
Oregano oil is a good anti-bacterial, anti-fungal, immune system booster, too. You can purchase it at any health food store.
These are my thoughts, I pray they are of some help to your rooster.
God Bless!