If you live in Oxford Street, or any other street, you will always stress the first word, the name of the street -- it's Oxford Street, not Oxford Street. However, if you live in Oxford Road, Oxford Lane, Oxford Avenue, Oxford Crescent or Oxford anything else, you stress the second word (Oxford Road, Oxford Lane, Oxford Avenue, Oxford Crescent, Oxford Way etc).
Various theories have been put forward as to why this is. Very broadly speaking, words, or elements of words, that can be understood from the context, are de-accented or unstressed, whereas the key, or unexpected or unpredictable, element is stressed. So, we have a green house (a house that is green - the word house is important here; we are talking about a green house as opposed to a green tree or a green box), but a greenhouse (a particular sort of structure - it's a greenhouse, as opposed to an alehouse). D Robert Ladd in his chapter 'English Compound Stress' in the 1984 book Intonation, Accent and Rhythm (Eds Dafydd Gibbon and Helmut Richter) says that out of all the words for thoroughfare - street, road, avenue, boulevard etc, street is the least marked -- it does not give much information (whereas we would expect an avenue to be wide, a crescent to be residential etc). He cites a letter that appeared in the literary magazine John O'London's Weekly in 1936: "Why, in speaking of thoroughfares, is it the custom to accent the proper name only in the case of a street? It is always Fleet Street, Southampton Street, but Shoe Lane, Farringdon Road, Fetter Lane". The paper's lexicographer, Jackaw, answered, "In a town, the great majority of thoroughfares are streets; street, therefore the expected word, needs no emphasis, and the stress goes on the street's name. Lanes and roads, being much less common, these words are naturally given at least equal stress with their distinctive names; convenience begets habit". In the early Old English period street was the commonest word for an ordinary thoroughfare. The first OED definition is 'a paved road, especially a Roman road'.
There is an added complication. I might say 'I live in Oxford Road' (I could also say 'on Oxford Road'), but I'd say 'I live on the Oxford Road', with Oxford stressed, and possibly with road spelled with a lower case r (I probably wouldn't say in here). This latter variant means the road that leads to Oxford, and the Oxford Road is treated here as a common noun, like greenhouse.