I don't remember current diesel prices, best bet is to buy when you think the price is good and quality is excellent.
You can get diesel (as in, from a
pump, not from glass bottles) in Papeete, Moorea, Raro, (don't know about Aitutaki), Viti Levu: Suva, Pacific Harbor, Nadi, probably others; Taveuni, Nuku'alofa, Neiafu, not sure about Ha'Apai group.
BTW Papeete is about the most expensive place in the Pacific for everything.
As far as other provisions, every town has a market.
Fish and vegetables and fruit is always inexpensive. The further you are from a major town, the lower the prices are. There are "real" grocery stores in Suva and Nadi, and you can get most regular provisions in the above named places.