It is possible for a cat to get a sore throat. See this link for more information but basically the article says:
When a feline has a sore throat, one of the most common symptoms is that the cat will start to swallow or gulp a lot. This could also include audible gulping noises.
Other symptoms of a cat having a sore throat include drooling more than usual because swallowing might be painful, or eating and drinking less food and water than usual. When a cat has a sore throat, they might also start to meow in a much hoarser fashion than usual, just like some humans sound raspy when they have a sore throat!
Since you don't know the history of these cats, I would call the vet and see if you can get him/her to prescribe you some medication to mix into their food. If they have never been vaccinated then they may have a virus that is causing them to be sick.
Here is another article about pharyngitis in cats, which could be causing the sore throat and lack of eating/drinking. If they have this then they will need an antibiotic. Hopefully if they are hungry enough, that will over power the sore throat and eventually they will eat.