(Note that I've moved this thread to a more appropriate forum.)
Judging from what I've seen at the two unis I've attended as a grad student in philosophy (ANU and UofT), you don't need more knowledge of logic to be accepted in a phd program in philosophy than in any other discipline. However, in some places they want you to have at least a good command of propositional and predicate logic by the time you get out, so they'll make you take an undergraduate course in logic if required (this was the case at UofT a few years ago). I don't think that training includes any set theory, alternate logics, etc -- it was the most basic course focused exclusively on logic (there were also softer courses like 'critical thinking' with a logic component, but these weren't enough to qualify for graduation). 

So, I wouldn't worry more about this for now. You've already learned what you really need to know for practical purposes, and doing more independent training isn't really going to help you for graduation purposes because they'll make you take a course anyway if you go to a place like UofT. That said, I would recommended reading the graduate prospectus of the programs you're thinking of applying to. 

Good luck!