"Our area is small."
Translation:Nasz obszar jest mały.
'obszar' just means 'area' and is totally vague
'strefa' is generally a 'zone', "A given area distinguished on the basis of a particular characteristic, use, restriction, etc." seems to fit for 'strefa'
'region' is usually something bigger, 'this region of the country' or at least 'city'
'dzielnica' is the easiest one to define because it's simply 'district' and it definitely is something on the administrative level.
I'm surprised how many people ask similar questions... the problem is, that all those words are rather vague.
"teren" is "terrain", and I would probably use it for "the terrain of something", like "terrain of our company". or "I have bought this terrain".
"obszar" is super vague. It's just some area. Maybe it's my desk. Maybe it's Russia.
"region" sounds like some part of the country, but it's also very unspecified. I guess just like in English.