OXF and OJD are the last 3 digits of the plane registration.

As already mentioned Air NZ have 3 different A320 seating configs, the newer A320neo, A320D (domestic) and A320R (regional). The A320D and A320R are both ceo aircraft (classic engine option). Up until last year the A320R aircraft typically only flew domestic flights as positioning flights for Trans Tasman flights. As more neo aircraft arrived to replace them several A320R aircraft were moved across to fly more domestic flights but they still fly international as well.

When you book flights you'll be able to tell the difference between all 3 as the seat selection is different. When you look at bookings however you won't be able to tell the difference between the A320R and A320D as they both just show as A320 - the only way is to look at the seat selection itself. For A320neo flights it shows A320neo under the aircraft type. The seat maps for all 3 are on the Air NZ website.

It is not uncommon however to get last minute aircraft swaps which is just a normal part of running an airline.