I am currently in Sydney and leaving in two weeks. My final destination is Atlanta.

I have 3 weeks to travel:

I wish to go to:
1. Syd - Great Barrier Reef (not sure airport Cairnes/Brisbane or something else)
2. Great Barrier Reef to New Zealand (probably Auckland)
3a. Auckland to Bangkok (might be easier to fly back to Sydney first?)
3b. I also want to visit Cambodia (thinking easiest to do Air Asia while in Thailand and fly back). I would prefer to go first to Cambodia if flights made sense
4. Thailand back to the US (final destinatio Atlanta)

I'd like to spend about
3 days in Great Barrier Reef
5 days in NZ
7 days in Thailand
5 days in Cambodia

Any tips on booking flights as far as combining etc?

You seem to be late in planning and booking this. Close in flights can be expensive.
For 21 days (3 weeks) you have far too many destinations. You will spend a lot of time just just getting to/from airports, at airports and flying. If you are determined to ago to Asia drop NZ.

1. BNE is long way from the reef. Only about half way from Sydney. You need to look at a map.
2. Do you mean Great Barrier island? And why?
3a. Many airlines from AKL. Look at the airport web site
3b. Many low cost airlines in Asia
4. A one way fare may/will be expensive. What research have you done?

No advantage in combining, what ever that means to you


Airlines that fly Australia (CNS* MCY* BNE OOL SYD CBR MEL ADL PER) to/from New Zealand (AKL WLG CHC DUD ZQN) (not from all airports to all airports).
- Air Asia D7 (OOL - AKL)
- Air New Zealand NZ (codeshares with VA) [Star Alliance] {* winter seasonal}
- China Airlines CI (BNE SYD MEL** – AKL CHC**) [Skyteam Alliance] {** November to March}
- Emirates EK (SYD CHC codeshares with QF). EK stopped A380 SYD AKL flights on 13 Jul 2017
- Jetstar JQ (owned by QF)
- LAN LA (SYD AKL) [OneWorld Alliance]
- Philippines PR (CNS - AKL)
- Qantas QF (codeshares with EK) [OneWorld Alliance]
- Singapore SQ (CBR WLG) [Star Alliance]
- Virgin Australia VA (codeshares with Air NZ & AC*) (Delta & AC* partner) [*= some routes in 2017]

By combining I meant multi-leg, or roundtrip pairs

Wondering if I can get a Sydney US flight with a stopover in New Zealand, trying to find it....

You will not get a multi leg, multi airline, multi county ticket at a reasonable price. Point to point will be far cheaper. Go and visit a living breathing real travel agent in a travel shop with your credit card.

In post 1 you stated Thailand USA. Is that now Sydney-NZ-USA??
Air NZ will be the only airline to offer Aust-NZ-USA, but expect to pay a big premium $$ for that privilege. AA, UA & HA fly NZ USA, so may be able to have a Aust NZ flight. But having that as the first flight may be hard/expensive. Go and visit a living breathing real travel agent in a travel shop with your credit card.

One way Aus NZ trans Tasman fares can be cheap. Do not see any advantages in trying to combine with a long haul.

You are trying to make this harder, and vastly more expensive, than it needs to be.
In this part of the world air fares are basically simple one ways, without the silly conditions so prevalent with USA fares.

could use LCCs for everything except to US

Within Australia/New Zealand you can also use miles, really good rates