Q: Are motocross bikes ok
A: No motorized vehicles. But as the above answer mentioned, there is an awesome Motocross track with miles of additional trails just several miles away, Kahuku Motocross.
A: I don't think so - but there is a GREAT set of Motorbike trails just a little further up the North Shore - search for Kahuku Dirt bike track/park. Miles of trails, and three separate groomed tracks. VERY responsible group of riders - they are on what is technically military land, and so they use it with respect to maintain the relationship.