Home project using current transformers
Measuring current isn't enough to find effective power, even if you know the voltage. 

\$ P = V \cdot I \cdot cos(\phi) \$

where \$\phi\$ is the phase difference between current and voltage. Only for purely resistive loads voltage and current are in phase, and then 

\$ P = V \cdot I \$

So you need to measure both current and voltage, not only to find the phase difference, but also because you need to know the voltage at each moment, because that will fluctuate as well.

There are special data acquisition ICs for this, which have two ADCs (Analog-to-Digital Converters) which measure current and voltage simultaneously and multiply that to get instantaneous power. Integration over time gives you energy (in kWh).  

You'll find ICs with a serial interface for a microcontroller which allows you to get real-time data, or others which give you a pulse for an energy unit, for instance 10 pulses per kWh.

Further reading
Energy measurement products at Analog Devices