I've done some Google search to know if people mostly use Oxford dictionary or the dictionary of Oxford. As I've understood almost everyone uses the first pattern.
I know native English speakers say, for example, both the University of Harvard and Harvard University. Why don't we use the dictionary of Oxford in the preceding example?
Often a university is officially called "University of Oxford" (or the like) but known informally as "Oxford University" for short. In fact, the University of Oxford uses both names (for example, its official Twitter account, @UniOfOxford, currently bears the name "Oxford University").
But you already knew that.
However, as for the Oxford dictionary... well, actually, there are many different Oxford dictionaries - the Oxford English Dictionary, the Oxford Dictionary of English, the Shorter Oxford Dictionary, the Concise Oxford Dictionary, the Oxford Dictionary of Quotations, the Oxford French Dictionary, and so forth. But as far as I know, all of them have the word "Oxford" before the word "Dictionary". Also, it is difficult to think of a dictionary whose brand-name comes after the word "dictionary". It generally comes before (Collins English Dictionary; Chambers Dictionary; Merriam-Webster's Collegiate Dictionary; Random-House Webster's Unabridged Dictionary).
So the official name of the dictionary is "Oxford English Dictionary" (or something else, depending which particular dictionary you are talking about), and almost all dictionaries are conventionally named with the brand before the word "dictionary" (unlike universities, where official practice varies).
Then add to that the fact that if you have a "dictionary of X", then X is generally the thing that you find within the dictionary. For example, you can have a dictionary of quotations, a dictionary of synonyms, a dictionary of place-names, a dictionary of French (also known as a French dictionary - though a French dictionary might mean a dictionary made in France, whereas a dictionary of French is unambiguously a dictionary of the French language). So, a "dictionary of Oxford" would suggest a dictionary defining words or names found in Oxford.
The usages are different.
I start with exemplification and analogy, and then continue to your examples.
The best and the most primitive example for English-learners is universitie's names.
e.g.: "University of Copenhagen" and "Copenhagen University".
Many teachers state that they're both the same.
NOOOOOOOT!!!
They're not. The first one, The University of Copenhagen, (like you mention - the noun of noun) implies the state university of the city Copenhagen, where the second one implies that the name (a proper noun) of the academic centre is Copenhagen, (like you mention - the noun + noun) like "Friedrich-Alexander University", the name of which is Friedrich-Alexander, and it's located in Erlangen - Germany.
The Dictionary of Oxford could be interpreted as the state, OR official, OR inclusive, OR ... dictionary of the area of Oxford.
The Oxford Dictionary however suggests the dictionary, the name of which is Oxford. This dictionary or I'd better say these dictionaries were a project, defined by the Philological Society of London, to recinsider the existing dictionaries of those times (late 19th century) specifically from Anglo-Saxon erra onwards. Hence, we see, it doesn't belong to a particular area or dialect or ..., but a variety of English language periods and the whole Britain.
