Hello, my name is***** and I have over 20 years of experience as a veterinarian. I am sorry to hear that Misty has a constant nasal discharge, voice loss, a sore mouth and is losing weight perhaps because he cannot eat normally and is burning calories fighting an infection.
If he were an older cat tooth and gum disease, a mass in his mouth, or organ failure with secondary nausea would be other possibilities, but seem less likely if he is only a year old.
Has he has been sneezing? Can you see any redness or ulcers in his mouth?
Herpes virus is the most common cause of upper respiratory symptoms in cats. But there are others too. Some upper respiratory infections, like Calici Virus, can also cause ulcers and these are painful, so they do cause a very sore mouth and throat, and that is definitely a possibility in a cat that is excessively drooling and losing weight.
If he will let you you can look for ulcers inside of his mouth, such as on his tongue and hard palate (roof of his mouth). If he has them the ulcers could be caused by Calici virus, which is an upper respiratory virus that can cause ulcers and joint pain as well.
Some cats get sicker than others and young, healthy adult cats seem to tolerate a respiratory infection and fight them off better than very young kittens or older cats. An upper respiratory infection in cats is just like a cold in you and I, and these are commonly caused by a virus. These are easily caught by breathing in virus particles in the air from a sneeze or nasal or eye discharge. Most of the time with supportive care they do come along.
You can help him feel better by adding warm water to his food to make it smell more (they don't eat if they cannot smell) as well as making it easier to chew and swallow.
Also the more fluids he gets the better. Offer tuna juice, low salt chicken broth, or a gruel of meat baby food and warm water. With the amount of nasal discharge he has doing dehydration is a real concern.
If he will come inside take him into the bathroom with you if you run a hot bath or shower as the steam will soothe his sore throat and airways and thin the nasal mucous making it easier to breathe.
If he will let you, you can use sterile saline to loosen the thick mucous and remove it. He won't like it but it will help him breathe and be able to smell his food better. You can also use sterile saline to remove eye mucous if it accumulates.
You can use Chlorhexidene oral rinses (like CET rinse) on the ulcers to keep them from getting infected by bacteria secondarily and keep them from becoming crusty and more uncomfortable.
Some lethargy is understandable, give him a safe place to rest as he needs rest to get better.
If he runs a high fever (more than 104F), has a green or yellow nasal or eye discharge, stops eating even with coaxing and clearing his nose and eyes, or starts coughing or having difficulty breathing then he needs a veterinary exam. I understand that he may be hard to catch and medicate so a long acting antibiotic shot may be a good option.
Sometimes these upper airway infections turn into pneumonia so that's what we need to guard against. In most cases antibiotics aren't needed and can contribute to a decrease in appetite so I don't tend to prescribe them unless I feel there is evidence of a secondary bacterial component. These include a green or yellow eye or nasal discharge, evidence of pneumonia upon listening to their lungs or an infection that lingers beyond the normal 7 to 10 days. Since this has gone on long enough for him to lose weight my fear is that he does have a secondary bacterial infection.
If you can catch him and have him examined I highly recommend testing him for feline leukemia and feline immunodeficiency viruses since his respiratory infection has lingered. These immunosuppressive viruses will make a simple infection much worse as they stop the immune system from fighting infections the way it was designed to do. If this has lingered beyond 7 to 10 days he needs a veterinary visit.
Here is a link if you want to read more about Calici virus: http://www.pet360.com/cat/health/calicivirus-in-cats/42gJj403b0idm8v6BjfOiA
If you cannot catch him to have him examined then you can certainly try soft foods and adding fluids/water to his food. Because Herpes could also be causing his symptoms you can give him an amino acid supplement called L-lysine at a dose of 500mg orally twice daily. If this infection is due to Herpes this amino acid interferes with virus replication and will shorten the infection's duration and severity. Good supplements to try are made by the Viralys brand which comes in a powder to add to the food or a tasty gel. If he doesn't have Herpes the supplement won't hurt him, but if he does he may benefit from it.
Let me know if you have any further questions.