Theoretically, you can't enter Canada until you've been granted 'rehabilitation':
http://www.cic.gc.ca/english/visit/faq-inadmis sibility.asp
However, New Zealand passport holders don't require a visa to enter Canada:
http://www.canada.org.uk/visa-info/visitor/e_v isa.htm
so you shouldn't have any problems entering the country if you simply keep quiet about your convictions.
New Zealand passport holders (without convictions) can enter the USA under the Visa Waiver Program:
http://travel.state.gov/visa/temp/without/with out_1990.html#countries
However, as you realize, your convictions render you ineligible for this, so you're meant to apply for a visa.
Only the US authorities can give a definitive answer as to whether you'd be granted a visa but I would think that it's extremely unlikely. (For example, I've seen a post on AB where someone was refused a visa because of two convictions for driving with no insurance). The US authorities tend to regard multiple offences extremely seriously. (If you'd committed your offences in New Jersey, where they operate a 'three strikes rule' you might currently be serving a prison sentence of between 10 years and life. The immigration authorities would look at your offences as if they were committed in the USA, not in the UK or New Zealand).
However, the US authorities have no direct access to the criminal records of any other country (except Canada, with whom they share a common database). If you're prepared to lie on the Visa Waiver form, you should be able to get into the USA without difficulty.
Chris