I am not an expert on energy saving II oil but some cars recommend using it as my 95 corolla does. I believe the theory is that it causes less resistance which mean less friction or something like that. I am not sure if its because the oil is thinner or light but that is the basic idea. I don't know if you should put it in your car if it is not recommended but that would be a good question.
I suspect that Energy Saving II oil is one of those designations they invented years ago while steadily improving oils over the years. I'm sure that any modern API rated oil will be at least as good and probably better FE than the best stuff available 10-15 years ago.
And along with that it looks like thinner is better for FE - as long as the car doesn't have leaky seals or bad rings. In that case a thicker oil usually seals piston pressure better and will leak less also.
So far I've been determined to use only the weights recommended in my car's owner's manual for my climate. I don't dare go to x-20 because the book offers 15-40 and 10-30. 10-30 is it for me, at least for now.
Currently getting +/- 50 mpg in fall weather. EPA is 31/39 so not too shabby. WAI, fuel cutoff switch, full belly pan, smooth wheel covers.