Why (Is of)

As far as I know, there's no case where you would use "it is of great use of", because you are saying "of" twice, UNLESS it is not being used to start a sentence. An example;

"At first sight, the definition brings about a neutral and functional explanationof the state, as it is of great use of a positivist, liberal approach."

It might help if you flip the words around in your examples to help you understand why you use the word "of." To rephrase Example 1:

"its quality standard is of a satisfactory level" becomes "the level of its quality standard is satisfactory". As you might be able to tell, before you rearrange the words, the phrase 'rolls off the tongue' a little better, and it makes a little more sense (when you rearrange the words, the sentence becomes a little 'clunky').

The second example is a little more poetic, and using word 'of' effectively removes or replaces certain other words, shortening the sentence. Here's how I think it could sound if you put all the words back in: "the picture is [one] of happiness, [but] the story [is] not." The problem with that example is that unless you already know the context in which the sentence is being spoken, it could mean several things, so I can't help more there.

This is not definitive - it's just how I understand it (and yes, English is my first language! )

Hi Ben

I would say that this structure simply omits words/ideas that have already been mentioned, and thus avoids unneccessary repetition.  Just as Christopher did, I'll use sentence 2 as an example:

- The picture is of happiness, the story not. =  The picture is (a picture) of happiness, (but) the story (is) not (a story of happiness).