I can speak to Micronesian typhoon preparation. Hopefully others can chime in if this doesn't apply to other parts of Oceania.

It may be best to start with this: typhoons in Oceania before it was possible to send airplanes for immediate relief were very scary. Even with packaged food commodities, local and global relief organizations, digital communication, modern weather prediction, and other staples of contemporary typhoon relief the storms can be terrifying. Take a look at this massive destruction caused by Typhoon Maysak in Ulithi just this spring. It'll take years to recover from that kind of damage.

Before colonial and post-independence government adopted the leading role in providing for relief from these storms, islanders on storm-affected atolls mainly relied on two things: keeping stores of preserved food where it could remain undamaged by the weather, and maintaing relationships with nearby islands.

Preserved breadfruit, which is called "mar" in Yapese, is fermented and buried in pits. There's a bit more information about it here. The breadfruit has a slightly poi-like flavor, and the pits would hopefully be unaffected by seawater or other storm damage and provide temporary relief after a storm. Typhoons often snap coconut trees in two or shear them of their leaves as well, which is likely to kill the trees for the long term. In the short term, however, the coconuts on those trees (at least many of them) tend to get knocked to the ground by the storm itself. The same may be true for pandanus, bananas, and other fruit trees. So the real crisis moment in terms of food isn't the immediate aftermath of the storm (when more food than usual may actually be available for consumption), but after that food runs out -- when taro patches have been contaminated by seawater, banana and coconut trees have been damaged, and canoes may have been wrecked or washed out to sea, making fishing difficult as well.

For those situations, many smaller atolls maintained ongoing relationships of tribute and exchange with larger islands. The largest of these in Micronesia was called the sawei system, sometimes missnamed as the Yap Empire. A string of outer atolls to the east of Yap gave tribute to one of Yap's three most powerful village chiefs, by means of a canoe voyage that made a circuit of those atolls once a year. The atolls gave tributes of food and other goods, and Yap gave back to them as well. The atolls then could seek relief from Yap in times of crisis -- either temporary resettlement until crops could be restarted on their home islands, enough food to get back on track, or something else. Incidentally, the reason the term "Yap Empire" is no longer used is largely because as far as anyone can tell Yap proper actually gave those outer atolls much more than it received from them. Elsewhere in Micronesia, single outer islands might have a similar relationship with a high island nearby or (as in the Marshalls) a string of atolls might have a similar relationship with one another.

Just to reiterate, however: damage from these storms could be massive, even with these measures in place. Low atolls could be entirely overrun with seawater, with all of an island's structures being destroyed, most of its population being swept out to sea, and survivors riding out the storm by clinging to a coconut tree swaying in the wind. Flying debris could kill or maim people as well. In cases of severe devastation, those same high island-low island relationships might come into play again -- with high islanders moving out to the low island to help them repopulate.