Today when there was a power cut I saw that the CFL light bulbs were flashing time to time at regular interval. I was amazed as there was no source of power to the CFL bulbs even they were flashing as if they were sucking energy from surrounding, collecting it and then releasing them with a flash. Why was it happening?
It's likely the power-cut wasn't a complete loss of power but a drop in voltage. The controller electronics in the CFL bulb base converts the 110/220V AC power into the voltage used inside the lamp, it can also store a small amount of charge. Depending on the design of the circuit it could also convert much lower, say 20-30V AC into the power the lamp needed - at least for a short time.
What probably happened is that the voltage dropped from your normal supply to some low value, say 20-30V as the grid tried to supply the same number of customers from a reduced supply. The lamp was able to store up energy from this low voltage and turn on. Then the voltage dropped to zero turning it off and the process repeats at random.
Modern supply system try and avoid this because it can damage appliances, they will typically sense a fault and go completely off until they are commanded to come back on. Bringing a power failure back online is quite complex. But if you live somewhere without an advanced intelligent grid you can get these voltage fluctuations - called "brown-outs" because they made an old fashioned filament light bulb glow dimly = brown
Do you know if you were getting beamed with microwave pulses? You can light CFL's up easily with an electromagnetic beam at the right frequency.
More seriously, do you have any big capacitors plugged into the same breaker's circuits? A capacitance/inductance/resistance circuit can sustain a fluctuating current for some time after the thing charging the capacitor has been disconnected.