Light consists of quanta(small packets of energy). Then how do we explain doppler effect of light the same way we do for sound? What is the valid explanation of light doppler effect which is consistent with the photon picture?

Someone more versed in university physics might be able to explain better, but I think it is just as simple as light travelling as waves means it is subject to the same treatment as any other waves - thus the Doppler effect applies. I am uncertain if there are any relativistic effects on the Doppler effect due to the speed of light.... but the wave particle duality of photons lets you consider it as a wave for travel and things like the Doppler effect and as a particle/packet for impact purposes.

 

I hope that helps - I am sure an actual physicist will add more or correct me if I am wrong.

The energy of a photon (or anything else) is observer dependent. So the motion of the observer changes the observed energy and therefore the frequency.

There's no problem. There is a frequency associated with a photon, such that E =hv. That frequency is shifted when there is relative motion (as I have confirmed countless times, since laser-cooling and launching a ball of atoms relies on this effect)

Doppler's effect is related to frequency of light. Even if light consists of photon, there is no difference to the frequency of the photons and they can be treated alike.

Particles can behave as both a wave and a particle. It's called the wave-particle duality.

 

If you really want a way of describing it in terms of quanta. Imagine I'm running towards you at 5km/h and I throw a ball towards you at 3km/h. I see this ball as travelling 3km/h relative to me but you observe its velocity as ~8kmh, thus you see it as having more energy.

 

Vice versa if I'm running away from you at 5km/h and throw it at 3km/h towards you, you'll see it as having less energy.