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As I understand the Angular Momentum of orbit is directed perpendicular to the orbital plane and is the cross product of position and velocity vector. In case of nodal regression, how does the position and velocity vary so that the Angular momentum is conserved ?

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Gravity goes both ways - the satellite pulls on the earth's bulge as much as the bulge pulls on the satellite - roughly speaking.

As the angular momentum vector of the satellite changes, so does the angular momentum of the earth change an equal but opposite amount (but wait!) So the total angular momentum of the satellite + earth is roughly constant - or would be if it was in a universe without any other objects.

There's a much larger amount of angular momentum exchanged between the moon and the earth, and Jupiter, and Venus, and the sun, and everything else.

These darn $\frac{1}{r^2}$ forces never reach zero, so everything is an approximation, and energy, momentum, angular momentum are never perfectly conserved locally.

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