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Welcome to JustAnswer, this is Dr. Christie.
1) Is the cat indoor only, or does garfield go outdoors too?
2) Has Garfield been tested for feline leukemia (FeLv) and feline immunodeficiency virus (FIV - aka kitty AIDS)?
3) Is Garfield eating and drinking normally?
4) If you look at Garfield's eyes, are they moving back and forth quickly?
5) Does Garfield seem to circle, fall, walk in one direction (right or left) more than the other?
6) If you look at Garfield's gums, what color are they - red, pink, pale pink, or white?
Many times when I see dark crusty stuff at the corner of the eyes (by the nose) and in the nostrils in outdoor cats, this can be due to dirt and debris collecting there. Certainly mucus from an upper respiratory infection (URI) can also collect in these areas. If Garfield is sneezing and coughing, then I recommend a checkup by your vet.
Garfield can be walking lopsided for many reasons. He may have an infection, poisoning, he may be anemic (low blood levels), he may have vestibular disease (causes neurologic signs as well as wobbly gait), or he may have a virus (like FeLv and FIV).
Ultimately he will need to see your vet as there is no way you can differentiate between these diseases. If he is FeLv or FIV positive, then he will need to become an indoor cat as he serves as a source of infection for other cats. His health will likely continue to deteriorate with these viruses, though cats with FeLv can live years with this virus. Your vet can recommend further treatment for Garfield.