Per Hawaii DOE, Homeschooling in Hawaii requires you to register with the local public school in your area, a "notice of intent" that you will homeschool through a FORM 4140.
This notice of intent acknowledges, the parent's intent to home school and allows the DOE to assist parents in their educational efforts. In addition, families are required to notify the principal if the homeschooling program is terminated or if another educational program is initiated.
HAWAII DOE homeschooling information.
Christian Homeschoolers. Classical conversations events around Oahu. CC is a national homeschooling program that uses a Bible based curriculum taught in a christian, classical tradition. Classes are geared for age 4 through high school. https://www.classicalconversations.com/events-near-you
Oahu Homeschool Moms has a great resources page with a lot of information about homeschool groups, events, and activities for homeschoolers.
Hawaii homeschool organizations and support groups.
Other homeschool support (not in Hawaii)
Here is a list of other Military homeschool organizations and support.