Let's say, I am sending a wave which has a Right Handed Circular Polarization and the receiver antenna has Left Handed Elliptical Polarization. So what will be the Polarization Loss Factor?
It depends on the ellipticity. Linear polarization is extreme elliptical polarization in one extreme, and circular polarization is the other. If your receiver is Left Handed Elliptical Polarization with very low ellipticity, it is nearly Left Handed Circular and you will get nearly no signal. If it is highly elliptical then it will be nearly linear and you will lose only 3 dB, but there will be no cross-polar rejection.
Look up Poincare's definition of polarization, and the Poincare sphere.
The polarization loss factor depends upon power output, gain, directivity of the transmitting antenna, and sensitivity of the receiver. For a high-power transmitting antenna with circular polarization PLF is very negligible.