I am sorry to hear that your fellow is drooling, lethargic, and sticking his tongue.
Is he able to eat and drink? With that amount of drooling if he cannot eat and drink he can become very dehydrated.
Does he have any red or raw spots in his mouth, either on his gums, on his hard palate (roof of his mouth) or under his tongue?
Drooling can be related to eating something bitter (a bug or plant) or bad tasting, having something caught between his teeth, or nausea.
Tooth decay and gum disease, a mass in his mouth, or organ failure with secondary nausea are other possibilities.
If you can see redness, or ulcers we need to worry about trauma of some type or a viral infection.
If he has been sneezing along with redness or ulcers then some upper respiratory infections, like Calici Virus, can also cause ulcers. These ulcers are painful, so they cause drooling, and that is definitely a possibility in a cat that is excessively drooling and lethargic, especially if he is refusing to eat drink too. The ulcers can be on his tongue and hard palate (roof of his mouth) as well as his gums. Calici virus, which is an upper respiratory virus, can cause joint pain as well, so these kitties are often lethargic both from dehydration and because it hurts to move.
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, in that these are commonly caused by a viral infection. These are easily caught by breathing in virus particles in the air from a sneeze or nasal or eye discharge.
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. He may be more likely to eat if the food is soft.
The more fluids he gets the better. Offer tuna juice, low salt chicken broth, run the tap if he likes to drink out of the sink. With the amount of drooling he is doing dehydration is a real concern.
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.
If his nose become very congested 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, let him rest as he needs rest to get better. If your cats normally go outdoors keep him (them) inside until they are back to their normal playful selves.
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. Given his refusal to eat and drink today I think an exam as soon as possible is best, ***** ***** he has a high fever and is very lethargic.
If his extreme drooling continues then he probably needs fluid therapy and pain medication from his veterinarian.
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 or deep ulcers in the mouth. 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 are also reasons for prescribing antibiotics.
I highly recommend testing him for feline leukemia and feline immunodeficiency viruses if his respiratory infection lingers. 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.
Here is a link if you want to read more about Calici virus: http://www.pet360.com/cat/health/calicivirus-in-cats/42gJj403b0idm8v6BjfOiA
Let me know if you have any further questions.