Three Phase Power
In three phase systems, there are three "hot" lines (L1, L2, L3). Often there will also be a neutral (N) and a ground (G). The neutral and ground should be bonded together at your service entry). The three lines are all 120 degrees apart from each other. Loads can be attached in either a wye or a delta configuration. In residential applications, often only two of the three phases are supplied (and different houses will get different pairs of phases as to balance them).
Delta
In a delta configuration, loads are attached between phases (and a neutral is not needed). This configuration is common for large motors and in industrial settings. In some delta configurations, a terminal on the transformer's secondary is grounded and provides a neutral. The ground terminal would be either one of the three lines or a center tap on the coil between two lines (creating a high-leg delta configuration since one of the lines is at a much higher potential (with respect to ground) than the other two).
Wye
In a wye configuration, loads are connected between a line and the neutral. Based on the question, I believe that this is the configuration being used. The power company supplies the three phases and a neutral, and the customer supplies the ground. Normally, the neutral is connected to the ground (which is bonded to metal rods in the earth, water pipes, etc...). If the load is properly balanced (meaning that there are equal currents flowing on each phase), the neutral currents will cancel out to be zero and the neutral would be unused.
However, it is rare that the three lines will be exactly balanced, so there would be a neutral current flowing based on differences of currents in the three phases.
The Root Cause
My hypothesis is that the neutral in the building is not properly connected to the power company's transformer. Without a good neutral connection, the neutral voltage is not held to earth potential (the ground connection usually has 1-20 ohms resistance to the earth). The neutral voltage will drift towards whichever line is the most loaded (as it forms a voltage divider). For example, if L1 has a large load and L2/L3 are lightly loaded, the neutral voltage will be pulled towards L1, causing the L2-N and L3-N voltages to became much larger than their nominal voltage.
So, the fix would be to repair the neutral connection between the building's breaker panel and the power company's transformer. This may be a bad connection of the neutral in the breaker panel, or a failing transformer. Repairing this could be dangerous because the problem might be in a section of cable that cannot be easily turned off (if the break is before the building's main breaker). Working with the power company to turn off your service or check their transformer will likely be needed.
Split-phase Systems
This problem has an analogue in the split-phase system which is common in the United States, and there are related questions on this site:
Quickest way is to turn off the mains and unscrew the socket and determine the polarity by the colours (Blue being NEUTRAL and brown being LIVE).
Otherwise if you have an EARTH connection nearby (copper pipe for instance) use that to determine which one has the highest RMS voltage from EARTH. Neutral shouldn't be that far off EARTH while LIVE should be 230V (ish)
(this is also why I like the British mains plug)
Best Answer
You've asked three related but not identical questions here which makes it hard to figure out what your real concern is and how to solve it.
The first two questions have a common issue which is whether and where the safety ground is connected to neutral.
I will answer assuming a US installation.
For your first question:
Safety ground and neutral are supposed to be tied together in one and only one location, the main service panel.
Sometimes you see receptacles where the receptacle's neutral and safety ground are both connected to the circuit's neutral because the house was wired without a safety ground. If you are trying to detect this, a visual inspection of the receptacle's wiring is the most reliable method.
Sometimes you see houses with incorrectly wired subpanels. In a subpanel, safety ground and neutral are required to be separated. Visual inspection is the best way to verify this also.
For your 2nd question:
maple_shaft's answer is good with one exception. The problem is he uses the ideal wire model where there is no wire resistance. In fact, 14 gauge wire has a resistance of about 0.25 ohms per 100 feet. Assuming the circuit is wired correctly and safety ground is bonded to neutral only at the main panel, a heavy load like a hair dryer will generate enough voltage drop across neutral from the load to the main panel to be easily measured. I personally verified this ten minutes ago.
For example, 15 amps will generate a voltage drop of 3.75 volts over a 100 foot neutral. If you put your voltmeter between safety ground and neutral at the same receptacle as the load, you will see this 3.75 voltage drop.
For your 3rd question:
Under a heavy load, the voltage between hot and neutral will be LESS than the voltage between hot and the safety ground. In the above example, there will be 3.75 volts less.