Single AC clamp can measure current flowing through a single wire in a non-invasive way. There are AVR/Arduino projects use such a clamp to measure house power usage. However, they use 3 clamps for 3 main wires that come into house breaker box. Unfortunately, I don't have access to separate wires in my breaker box. I can only access main power cable that comes to my house through the roof, and that cable has all the wires inside itself (is this a good assumption?) without possibility to separate them. If that is so, then the question is can I use a single clamp on that main cable for my own little power usage measurement AVR project, and if I can then is there some reason for it to be less reliable then 3 clamps solution?
No, you cannot use a clamp meter on both the live and neutral wires at the same time. Current flowing back through the neutral wire will effectively cancel out current flowing through the live wire, and it will read 0 amps (assuming no current is leaking out anywhere).
One clamp around the live wire should give you the reading you want.
I don't know why you would need 3 clamps though, unless you have 3 phase coming into your building, in which case you'll need to sum the 3 separate currents to get the total current used.
Clamp meters measure the total current moving through them (i.e. currents moving in opposite directions cancel out). So if you were to put a single clamp around all of the conductors connected you house to the grid, you would only measure the difference between the current entering and leaving your house, this is often referred to as leakage current, and usually indicates a fault (if non-zero).
Note that just because you have 3 conductors doesn't mean that you have 3 phase power, for example in the US most houses are supplied with two phases (usually fed by a single phase in the distribution network), so the 3rd conductor is actually the neutral (not to be confused with ground). In fact in a residential environment, if you actually had 3 phases you would expect 4 conductors (3 phases plus neutral), this is known as a Wye (Y) configuration. While it is possible to have 3 phase system with only 3 conductors, that requires the load on each phase to be virtually identical, which isn't really possible in a residential system.
As said already, you cannot use a single ordinary CT clamp around both live and neutral wires. The total current it measures would be (close to) zero as the current in the neutral wire flows in the opposite direction.
However, for the sake of completeness, there are ways when putting multiple wires at once into a single CT clamp makes sense:
Wires of the same phase. If you made sure that all the wires you want to measure are live wires of the same phase, you can put them into the same CT clamp and it will correctly measure the total sum of the current in each of them (reference). Since they are of the same phase they have a combined sine wave current form, so this will also work with the cheaper CT clamp meters that "use a rectifier circuit which actually reads mean current, but is calibrated to display the RMS current corresponding to the measured mean, giving a correct RMS reading only if the current is a sine wave." (source).
Wires of different phases, with a true-RMS meter. In your case, if your grid electricity connection contains three live wires of different phase, you could route these (and these only) through one clamp. The total current will only be displayed correctly if you have a "true RMS" clamp meter, which means that it will read many current samples in one cycle and average them. This works independent of the waveform, which in this case of combining different phases with potentially differing currents is not a sine wave (so the cheaper mean current measuring clamp meters cannot be used, and recalibrating them is also not possible as the different phases can have varying currents over time, resultingin different waveforms of the total current). The AVR / Arduino projects probably do not implement a true-RMS current meter, though (but they could).
(Important: While this part of the answer is logical to me, I did not test it. Please correct if required, I made this answer wiki for that reason.)
Live and neutral together, with a special CT clamp meter. As referred by Wikipedia:
A relatively recent development was a multi-conductor clamp meter with several sensor coils around the jaws of the clamp. This could be clamped around standard two- or three-conductor single-phase cables to provide a readout of the current flowing through the load, with no need to separate the conductors. (source)
An example of such a device is the Megger MMC850:
Unlike conventional clamp meters, the MMC850 has a complex array of Planer magnetic sensor coils to calculate the current flowing in the conductors of multicore cables with either 2 or 3 cores (source)
Still no match for your case of three phase wires, neutral and earth, and for sure not a feature in an Arduino project. But interesting.
(yes i know this post is old, but still relevant since the Megger MMC850 has been discontinued and no alternative has presented itself)
Someone has been fiddling with hall sensors an made a sensor board. It might be a solution:
I would agree, curent coming back on the neutral conducter is esentially flowing in the oposite direction and nulling out the magnetic field produced by the load on the line conducter. For example if you have 4.23a drawn through the line conducter and 4.22a back on the neutral, your clamp meter in theory would read 10ma which would be the leakage current. However this is all theoretical, in actual practice the chances are that the line and neutral fields would probabily not be perfectly canceled out due to positioning within the outer sheath and tolerance of your meter..