I believe that you made a mistake in your post when you said:
If your problems persist and the noise continues, the problem will be within the water lines - which sounds more like "water hammer". That is when air gets trapped in the lines and "hammers" when the valves are turned on/off.
If water hammer is the problem, CraigFL suggests draining your system which I agree with.
You seem to be saying that it's the trapped air that's causing the problem, and that's not correct.
The newbies are gonna wonder, for example, exactly how the air trapped in the water pipes causes noise to be made, and why they don't hear a similar noise whenever air gets into other water pipes, like drain pipes.
Also, oxygen is continually being produced inside the water heater when you heat cold water. Cold water will hold more O2 in solution than hot water, so often O2 gas will be driven out of the cold water when it's heated. In fact, if you look for it, you very often see tiny "blasts" of compressed gas (air, maybe?) come out of the hot water faucets in your home when you're running hot water. They're very short lived, but they're there. So, why wouldn't EVERY house with a water heater have water hammer problems?
And, the sharpest newbies are gonna ask: "Why doesn't the air come out when you run the water?" (And they'd be right of course.)
So, lemme explain water hammer...
Water hammer is really just the shaking of water supply pipes as a result of abruptly stopping the flow of water through them.
You see, water is heavy, and when it's flowing through a long pipe, it can have a lot of momentum. One of the laws of physics is "Conservation of Momentum", which basically says that momentum is energy and energy can neither be created nor destroyed. You have to have the same amount of energy after an event as you did before it. A figure skater turning slowly with her arms out and then spinning faster as she brings her arms in is an example of Conservation of Angular Momentum.
Some people might ask "Where, pray tell, is the law of Conservation of Momentum when a Boeing 747 nose dives into the ground?", and so it's probably better to call it Conservation of Energy rather than Conservation of Momentum.
So, when you have water running quickly in a pipe, then the momentum of the water wants to keep it going at the same speed. But if a suddenly closed faucet is preventing that, then all the water molecules pile up against an elbow or tee or valve or whatever it is in the pipe that's now stopping them from continuing to flow at the same speed. It's just the same as if you have a crowded bus come to an emergency stop. All the people inside would pile up against the front windshield of the bus, which is what's now stopping them from continuing to move at the same speed as before. The momentum of those people is all born by the windshield, which would pop out of the bus if it could.
When the water piles up against an elbow or a tee, the momentum of the water is imparted to that elbow or tee, and the pipe moves as a result. When the pipe moves, then it'll spring back to it's original position, and it's the shaking of the pipes as a result (and the resulting bouncing around of the pipes against the walls or joists) that makes the noise we call "water hammer".
Water hammer can sound like your pipes are shaking themselves loose inside your walls, but it really doesn't do any harm. It just sounds like there's being harm done.
Installing surge arrestors on pipes that have water hammer helps prevent the problem because they use the water's momentum to compress air rather than move the pipe. That is, much of the energy of the water is used to compress a gas in the surge arrestor, and so less energy is imparted to the pipe. The pipe moves less and there's less bouncing around and so less noise.
But, really the best solution is to fasten down the pipes more securely so they don't move in the first place. (in that case, the momentum of the water goes into stretching the copper pipe an infinitesmally small amount before it snaps back to it's original length) ((otherwise, you'd be destroying energy if the water's momentum merely "vanished" cuz the pipe didn't move))
You can prevent water hammer that occurs on the supply lines going to faucets simply by closing the faucet slowly. By reducing the speed of the water gradually, you have less momentum available to move the pipe.
Water hammer tends to be worst on the supply piping going to dishwashers, clothes washing machines and toilet tank ballcocks (fill valves) because of the way the valves in these things work. These valves close very rapidly, and that doesn't allow for the momentum of the water to be reduced gradually like you can by closing a faucet slowly.
Draining the water out of the piping will only help if the poster has "home made" surge arrestors on his/her water piping. You can make such a thing by simply providing some extra vertical copper pipe at the tops of vertical risers so that air will naturally be trapped in that additional pipe when the system is filled with water. The problem with these home made surge arrestors is that they are prone to becoming water logged, and therefore ineffective at preventing water hammer. Good quality surge arrestors will have a piston or diaphragm inside them that forms a physical seal between the water and the gas, and that prevents them from becoming water logged.
So, water hammer is all about physics and energy. Air plays no role in creating water hammer. In fact, air trapped inside the supply piping would actually help reduce water hammer because that air would have less momentum than water, and the momentum of the water upstream of the trapped air would go into compressing that air rather than moving the pipe.
So, it's the momentum in the pipe, not the air in it, that causes water hammer.