More than 30 beneficiaries of the Cash Transfer Programme were taken to the bank Thursday where they cashed their cheques.
Registration of other families from Ambae who are temporarily living on Santo are continuing.
Evacuees on Maewo island will also be assisted.
The displaced families will be able to food, hygiene supplies and pay school fees for the next three months.
The government ordered a mandatory evacuation of the roughly 10,000 people on Ambae in August due to volcanic activity.
Oxfam's Pacific Cash and Livelihoods Lead Sandra Uwantege Hart earlier told RNZ many families are living in temporary shelters on Maewo and Santo, and it is not clear when they will be permitted to return home.
She said giving Ambaeans cash to spend locally will help them meet the needs they have.
Hart said there are between 7,000 and 7,400 Ambaeans - or 64 percent of the population of Ambae - now living on Santo.
In Maewo, where approximately 2,500 Ambaeans are living, Oxfam will begin an assessment next week to evaluate the market.
Hart said New Zealand's Ministry of Foreign Affairs and Trade is providing Oxfam with most of the funding, which will translate into support for more than 80 percent of the people who have been evacuated from Ambae.
Photo Oxfam in Vanuatu