EDS study would be very helpful in your case to understand the composition. Apart from, XPS would also provide  % of each constituent.

Correct, EDS and XPS would be very helpful to get requested information.

XRD, SEM, and spectroscopy techniques can be applied for qualitative and quantitative measurement of oxide phases.

We did EDS analysis and we got % O, %Zn, and % Mg, how can we decide the correct percentage of Mg, MgO, Zn, ZnO?

MgO = 24 +16 = 40 g; %Mg = 24*100%/40 and %O= 1 - %Mg

ZnO = 65 +16 = 81g; %Zn= 65*100%/81 and %O= 1- %Zn

Let EDS give %Mg=x, %Zn=y and %O=z

%O is important - that will tell %of Mg and Zn converted to MgO and ZnO

Use the mass balance to get the percentages..

Dr Ram Krishna thank you for your answer but it is not that easy because what portion of O will be for MgO and what portion will be for ZnO. Moreover, It seems that ZnO2 also could be formed that is why I am asking. 

Ok, so better first confirm what are the exact phases in the system existing - using multiple approach XRD, SEM, TEM and phase diagram. Then in the bracket of confidence you can use EDX data to confirm the weight% of components. By the way, can you please share %O, %Mg and %Zn have a look to get %ZnO2, ZnO and MgO. Thanks.

I will try to use XRD and EDS. (S)TEM might not be appropriate, as your sample might not be uniform in composition because of multiple possible phase. So bulk analysis using EDS to get composition, and XRD to see what phase(s) are your samples. If your samples has different composition, you can do multiple point EDS spectra across the sample, but you can also do AES to see whether the composition is uniform in depth. You may also consider to use XPS to compare/reinforence with the XRD pattern. 

Thank you Dr we cheng Zhong for your answer. I suggested in situ characterization approach so we will test Zn alone, Mg alone, and mixture of them with their oxides an see what will we get.