Hey, I was in the same position as you last year. I teach history and social studies and though I had the advantage of being NZ trained at Auckland Uni I had the disadvantage of being a brand new teacher with no experience.
I applied to 14 schools for a permanent job and got not a single reply or interview. So then I applied to a dozen schools for relief teaching. Two of them told me I was on their list, but I wasn't called in until week 9 of term 1 and only then because one school was having a massive trip with a dozen teachers on it. In all of term 1 I was called up 5 times. However, I was on the North Shore of Auckland, my friend in South Auckland was being called in every single day, though he had the big advantage of having attended his main school as a student just a few years earlier.
I kept applying for regular jobs and finally got an interview which resulted in my getting a Long-Term Relief position from the start of term 2 at a high school just minutes from where I live, and not one of the ones I was on the relief list at. At the end of the year I was made permanent in the position.
While I was working there I discovered that the school only used two or three full-time relief teachers, all who had once been full-timers at the school and semi-retired or took maternity leave. It seems most high schools do that.
The other piece of bad news I have to tell you is that I happen to know that the number of students studying to be history and social studies teachers at Auckland Uni in 2009 was double the number in 2008, so there is way more competition out there. Hopefully because of your experience you will be chosen over them even though you're coming from overseas. Good luck!
05/07/06 Arrived in NZ on Student Visa
24/03/09 Granted Work Visa
22/04/09 EOI selected, 155 points with job offer
04/06/09 Decision Successful
02/10/09 ITA submitted
24/02/10 PR Approved