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.