new home; new residence
Refers to the home someone has newly moved into, newly built, bought, or otherwise started living in. Common with verbs such as 引っ越す, 移る, 構える, and 招く.
We are moving into our new home next month.
I invited my friends to my new home.
We're planning to move into our new home next month.
We set up our new home in the suburbs when we got married.
We invited our friends over to our new home for a party.
I'm looking for a new home near the station.
自宅 simply means one's own home with no implication of newness, unlike 新居 which stresses that the home is new.
旧居 refers to a former residence one has left, the opposite of 新居, the new home one has just moved into.
新築 describes a newly built building or the act of building it, while 新居 describes the home as the place someone has newly started living in, whether built new or not.
A Sino-Japanese compound of 新 meaning 'new' and 居 meaning 'residence' or 'dwelling'; the spelling transparently matches the modern meaning.