Bear in mind that 'by' in Norwegian can refer to places that would never be called 'city' in English. If you look up 'liste over norske byer' on Wikipedia, there are several places that have 'bystatus' with only a couple of thousand inhabitants. They could easily hold a collective party!
Whether or not a place calls itself a city is politically decided. There used to be regulations about size and number of inhabitants to get city status. I think most people think as a minimum a city should have a Main Street. The term village (landsby) is not common in Norway but after travelling a bit abroad I have taken to call small places that. Especially small places that call themselves by
Tettsted, is the term closest to village (my google translate says town = tettsted). I do feel a village has more of a centre than most Norwegian tettsteder, as rural areas we call tettsted nowadays has few shops other than (perhaps) a gas station.
En bygd is pretty similar to en landsby. Which is not unlike et tettsted. I'd say the first is the smallest and the third the biggest, but that is not science (after all, being a city is politically decided and has nothing to do with population or commerce or anything)