As stated by Timatic, the database used by airlines, Americans do not need a visa for New Zealand.
Visa required, except for Nationals of USA for a maximum stay
of 3 months.
As for Vietnamese:
Visa required, except for Passengers with a valid “Authority
to Return”, or a permanent residence visa, or a resident return
visa issued by Australia, permitting an indefinite stay in’
Australia.
So if you hold any of these documents, you can enter without a visa. Otherwise, you need a visa
Credit:stackoverflow.com‘