"Where is your district?"
Translation:Gdzie jest twoja dzielnica?
"dzielnica" is simply a district. An area with clearly set boundaries on the administrative level.
"osiedle", according to Wiktionary, translates into subdivision/housing estate/settlement. I have no clue if those are accurate translations, frankly. In cities, 'osiedle' is generally a terrain of closely-built buildings, most often blocks of flats (but not necessarily). Sometimes such a terrain is surrounded by a fence, so only the people who live them can enter osiedle.
"obszar" generally just translates to 'area', it's rather a vague term.
"okolica" is like 'the neighbourhood', or 'the surroundings'. It's also quite vague and subjective (how far is too far to not be called 'okolica'?)