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:
Typically yes, you can run a single phase load from a three-phase service.
An issue would be if it is a line-to-line load or a line-to-neutral load, and whether a neutral is present.
Another thing is to make sure the voltage is correct for the application, and whether a high-leg is present (not sure if this applies in your area).
Best Answer
That is a simple "open ground", or "open earth" situation. The safety connection to "earth" is open somewhere in the circuit.
This is a problem that should be corrected. May I ask what prompted you to make these measurements?