It's highly likely he's suffering upper respiratory infection/disease which is likely occurring with or in conjunction with feline herpes infection (no, you can't catch it)
Not uncommon occurrences, often presenting with symptoms that can be confusing to their human companions. Upper Respiratory Infections or Disease may look like something else. The cats 3rd eyelid may be showing (looking like a cloudy, white covering coming from the inside corner of their eye), the cat may vomit or have different stools (diarrhea or even hard, strained movements). It may appear that the cat is trying to cough up a hairball, but nothing comes out, or what does could look like phlegm/mucous. Sometimes they can't keep food down very well and vomit soon after eating. Another symptom may be going off their food altogether. If they can't smell it, they are not likely to eat it.
Upper Respiratory Infections may have underlying causes of bacteria or virus (even fungal or parasitical) and there could easily be a secondary infection happening. Since left untreated it could spread to other systems, turn into pneumonia and possibly become life threatening, it's always the safest suggestion to have a vet evaluate the cause so it can be properly treated. By waiting, the condition may just become more complicated and a great deal more costly to treat.
Look here for more info about what happens http://www.marvistavet.com/html/body_feline_upper_respiratory.html
Since this is a stray - you may qualify for no cost/low cost feral rescue care:
Places you can begin looking
http://www.imom.org/
http://www.mspca.org/site/pp.asp?c=gtIUK4OSG&b=126801
http://www.animaladvocacy.net/shelters-rescues.html
http://www.lovethatcat.com/spayneuter.html
Don't forget to call your local Humane Society for guidance as well. If you have a Pet Smart in town, they often have the numbers for rescue organizations that may also help, at least with recommendations for where (or who ) to go.
Good luck and God bless for caring so much about this little guy! Very good job!
Own Animal Care org.
Animal Rescue&Care Org Owner; Animal Care author; Animal Behavior Consults.;Cert. Avian Specialist;