1 nCap. Name of the most populous of the Hawaiian Islands and the seat of Honolulu. The name has no meaning (see Pukui, Elbert, and Mookini; 1975, 262). See saying kau poʻohiwi, and epithets, Oʻahu (English-Hawaiian). [PH]
1 prop nCap. Most populous of the Hawaiian Islands, 40 miles long, 26 miles wide, with an area of 608 square miles and a 1970 population of 768,561. Honolulu is the major city and State capital. See Appendix 6.8 for a refutation of a meaning often quoted, 'gathering place'. Epithets: Oʻahu o Kākuhihewa, Oʻahu of Kākuhihewa (an ancient chief); Oʻahu a Lua, Oʻahu [child] of Lua (Lua slept with Papa after Papa became angry about husband Wākea’s infidelity; Lua gave birth to Oʻahu; HM 302).
O'ahu can be thought of as a place like a city or a province instead of just an island. When we talk about what city or maybe province or state where someone works, we say "work/s in'. "He works in Berlin." "I work in California." Even for a country, we'd say "They work in China." I think the verb "work" is the key to determining the preposition here. (Not saying that "on" is incorrect, btw, just saying that I don't think "in" is wrong in this context. We obviously don't stand in an island. Taken literally that boggles the mind.)
I always thought we could get over the problem of what to Call Hawai'i Island in conversation. To say you live in the State you could say "I live in Hawai'i" to say you live on that Island you would say "I live on Hawai'i" no more pilikia about saying 'the big island' etc.