As a train of gravitational waves generate from its source and passes through, is it stretch and compression of space-time with same angle all through the distance it is passing and damping over time, or is it better to say that, is there any angle for parameter of stretch and compression in gravitational waves?
Gravitational waves, far from their sources are (in General Relativity) transverse. That is, the stretching and compressing of space always takes place at right angles to the direction of wave propagation.
In the plane at right angles to the direction of wave propagation, the direction of maximum stretching is determined by the polarization of the wave. A wave can in general be composed of a mixture of two polarization states that are rotated at 45 degrees with respect to each other, known as plus and cross polarization respectively. The lines of the plus and cross mark the directions of maximum stretching and compressing.