The only slight difference I might discern would be that a book about or on English grammar might not be a book with all the grammar rules. It could be a book giving the history of English grammar, how it came about, how it differs from other languages etc. That is just one interpretation though.
A book of English grammar would be the kind of book that the students here use, containing the rules and examples and in which one can look up a grammar point.
Student or Learner