Preposition with Night

At night vs. By night; at night vs. In the night; night after night vs. night by night

The difference between “at night” and “by night” is that the former shows time (‘We work during the day and sleep at night’), whereas the latter suggests method or the conditions under which something is done or takes place (‘Burglars and poachers work by night,’ ‘In order to avoid the heavy traffic on the roads, some people prefer to travel by night’).

The difference between “at night” and “in the night” is that “at night” is used when talking about what generally or regularly happens then (‘The noise of the traffic keeps me awake at night’), whereas “in the night” is used when talking about an event that happens at some time during the night (‘There had been heavy rain in the night’).

"On" is used as in “on the night of 10 January/January 10, (on) Saturday night, (on) that night, etc.”

“Night after night” expresses the idea of a succession of nights taken individually (‘Night after night she sat by the bed of the sick child’); “night by night,” on the other hand, represents the succession of nights as one continuous period or series (‘Night by night the policeman paces the streets’). Cf. day by day.

Overnight

(1) During the night: e.g. to travel overnight. Hence an over-night journey.

(2) For the duration of the night.
We stayed overnight at a hotel.
Cf. Over the weekend, over Christmas, over the New Year, etc.

Reference: English Prepositional Idioms (by Frederick T. Wood).