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Humming noises in your house can occur while using a faucet or flushing a toilet.  If you can run water anywhere in your house and you hear a humming noise the chances are the "house pressure regulator" is making the noise.  Make sure the pressure adjustment locking nut is tight.  If it is than you may have to replace the regulator.  If you don't have a regulator it's quite possible the water meter itself is making the noise even if the meter is outside by the street.  Noise resonates/carries through the pipes.

Banging noises come from when a faucet or some water dispensing device is shut off abruptly.  When water is flowing through the pipes there is an energy type of action going on.  When the faucet shuts off abruptly that energy needs to go somewhere which is in the pipes, causing the pipes to shake.  Poorly strapped pipes are more susceptible for these noises.  Check around for loose pipes in your basement or crawl space and secure as necessary.  They also make mechanical devices call hammer arresters that you can install into the main cold pipe of your house.  When a faucet is shut off, the energy is softened by the hammer arrester (it's like an air chamber).  There are a couple of different kinds available.  My favorite is an expansion tank.  It's about the size of a basketball.  It also comes in handy for water heaters that commonly expel water from the safety (T&P) valve.

Ticking noises are as bad as a leak in your pipe in the wall, a drip from a faucet, or trickier yet, inside the toilet tank.  Inside the toilet tank is the fill valve, where the water comes in to refill the tank after a flush.  There is a small hose, in most cases, that goes from the fill valve to the overflow tube in the center of the tank.  Sometimes after a flush the water coming out of the hose never completely shuts off and just keeps dripping in the overflow tube.  If you're in the bathroom and it's quiet you may be able to hear it.  What's happening is water is being  siphoned from  the tank and down the tube.  When the tank level gets low enough you get a "mysterious flush" syndrome. You may want to replace the fill valve or adjust the little hose so it doesn't go below the level of the tank.  Fluid Master (found at your local home store) makes a clip that goes on top of the overflow tube that the little hose clips on to so the problem doesn't happen at all.