Hi MML,
As far as I can see most of those 'S's are correct. The way it is
might be okay but I think taking the 's' from 'methods' and changing 'are' to 'is' would read a little better, as would making the whole thing two sentences instead of one. Maybe moving some words around might also help - it seems a little 'bulky' at the moment. There are two extra ways I can think of putting it. Either way, if someone reading this already knows it's referring to more than one label it would be better to take the word 'two' out. Here's the slightly altered original first sentence with the other two ....
"The expression method of the nutrition labels is different."
"The nutrition labels have different methods of expression."
"The nutrition labels are expressed differently".
In the second sentence it would probably be better to change 'have' to 'need' and take 'the' out - "We need to do some calculations to enable comparison of nutrient contents." This could be phrased, "We need to do some calculations to compare nutritional content." (Or "....compare the nutritional contents")
Does the whole thing express the original idea/meaning? - "The nutrition labels have different methods of expression. We need to do some calculations to compare nutritional content."
Just my 'take' on it!