No, you cannot sue if a stray dog bites you. The dog has to have an identifiable owner.
We do have situations where the dog is possessed and controlled by more than one person, so for example, maybe a couple of roommates purchase a dog, and that dog ends up biting our client. Sometimes there is a dispute among two or more persons as to who owns the dog, and the dog will carry with it documents that state the identity of the registered owner. However, beyond that sometimes the registered owner will make an argument that others co-owned the dog and were just as responsible for the dog as he or she was.