Can I get into computer science grad school without a strong math background?
The only way to know if you can get in is to apply to a few programs and make your best case. There are some aspects of computing that require less of mathematics and others that require more. 

But, don't make the mistake of conflating computer science and computer programming. Programming is only a tool, if a necessary one, for more important things. In particular, some of the things you have probably missed are deep study of algorithms and, especially, algorithmic efficiency and complexity. These are pretty much dependent on mathematics. If you were to be accepted into a CS grad program you would be competing with people who have studied this before, never mind graph theory, for example. 

There are, however, some aspects of CS that are very tied up in things like human psychology and physiology more than mathematics. There are universities that focus, especially, on human factors. Even language design can learn from such things. 

All is not lost, but it would be a pretty hard road even if you are accepted. You will need plenty of other evidence of the likelihood of your success to get in the gate, however. There is a lot of competition and most of it has followed a more standard path, so many graduate programs expect and depend on that background.



As for the usefulness of math in CS, note that discrete math, probability, and logic are more central than calculus, which has some, direct application, but is only occasionally essential (say, in theoretical work). 

And for advanced work, Category Theory may be needed. Deep stuff.