What 5 things would you do to add more power to a pre 2009 5.7L. (short of forced induction, turbo, nitrous)?

Eagle Heads And intake manifold, SRT 6.1 Cam , Headers and A good tune.
If the Eagle heads are too much compression, then go and get 6.1s.
You can port the pre Eagle heads and get good results.
that's my 5.

I pretty much agree with ric. Also I would not be afraid of the compression, I measured one and it came to 11.5, the 6.4 has 10.9 from the factory so your only 1/2 point over that, run premium pump fuel, you will get improved MPG from the compression and it will not cost much if any more in the end. These motors are very detonation resistant.

Lets say a guy has a 2007 Ram 1500 and has to pass emission testing. Can the above possibly comply ? In California, the testing consists of a scan of the OBD2 system and a visual smoke test. If the computer shows no codes, it passes.
What kind of power increases can one expect while still being compliant? The stock rating is 345 HP.
I have 306,000 miles on mine. It runs fine but has surely lost some power. It leaks nothing but burns oil.

the headers may give you a code for "slow cat warm up" "slow O2s response" or something to that effect and will not bolt right up to the exhaust, if were talking shorties they aren't worth the bother anyhow. A tune may be able to eliminate that but if they visually look it won't look stock and they may need to see a carb EO number. Maybe you help the exhaust and still look stock enough with an exhaust system from an 09 3/4 or 1 ton hemi truck, it flows way better and looks like, well a stock system.

The cam might give you a misfire code but I have not seen that problem myself. Again a tune should be able to cure that.

Overall you should be able to do all that with no issues except possibly the headers. Obviously don't mention that you have a non stock cam or heads while at the testing station.

You probably should be looking at a high flow intake also as you need to flow a lot more air in to match the higher flow after it, probably need to find one that has a carb EO number or put the stock one on during testing. They still have a looky around under the hood don't they?

I am a bit embarrassed to admit that I am out of the loop on what they actually do. I recall before OBD2, they did a visual check to ensure all equipment was in place, a probe in the tailpipe to measure emissions and a vacuum check of the gas cap. Nowadays, all that I am sure of is that they do not sniff the exhaust on OBD2 vehicles.
The truck is not a slug but I figure that if I do rebuild an engine for the truck, why not step it up a little.

With tuning software you can actually mark stuff not to report... which won't show up in an emissions test, meaning it would pass. I'm not saying to do this, probably illegal, but can be done.

Basically emissions checks for stored codes and there are readiness monitors. Like for o2 sensors, evp system etc.

There are some C.A.R.B legal headers, the 6.1 cam won't throw a code, if tuned , some one like Jay Green can write you a tune that will work, and even spec a cam that will pass.