You will have to use a Oneworld award since you will be arriving into and departing from 2 different award zones. The total miles traveled will be just over 17,000. Oneworld awards count the mileage from departure point to destination (i.e. ORD-HKG) regardless of where you connect along the way as long as the connection is less than 24 hours, otherwise it becomes a stopover and must be included in the mileage calculation. This particular case will be a Distance Zone 6 award as found on the Oneworld chart, allowing for 14,001 to 20,000 miles. The cost for this award will be:

Economy class: 100,000 miles
Business class: 130,000 miles
First class: 180,000 miles

Even if you want to make a stopover in LAX, it won't affect the award cost as the total mileage by adding in LAX still falls in the same 14,001 to 20,000 mile range. And oddly enough, the mileage SYD-ORD is exactly the same as SYD-LAX-ORD at 9232 based on the Great Circle path.

The business class award is certainly a good value, considering it's only a 30,000 mile premium over economy. Only problem you may have is finding award availability on the QF flights from SYD to LAX for premium cabins. This would be a fun trip.

Keep in mind that if you add in the HKG-SYD sector, your total cost for the award would only go up by 20,000 miles for economy and business and 50,000 miles for first class to 120/150/230 for the entire trip, based on 21,606 miles using ORD-HKG, HKG-SYD, SYD-ORD.