Hi Folks,
With more analysis the culprit turned out to be Google PageSpeed module for servers. So there is no issue with EWWW plugin, that does a fabulous job.
I am not sure about the interoperability issue between EWWW and PageSpeed Module (basis my earlier comment on activating and deactivating the plugin) but that Google PageSpeed module does cause a lot of issues with images and themes.
Thankfully with this I even found the reason why some of my other WordPress sites would have random issues with images etc.
To conclude EWWW works great.