Did an analysis of all available North American bird strike data a few years ago for a report and one of the data sets was day vs. night. The data showed that there were slightly higher numbers of strikes at night vs during the day.
Normalizing that for aircraft movements then shows that the strike rate is higher at night than during the day.
Lots of migratory birds fly at night to take advantage of favourable winds. The bad news is they sometimes fly quite high and their weights and flcokcing characteristics exceed the airframe, windhsield and engine certification standards.
Yes, birds do fly in IMC. No the radar does not have any effect on them.
There have also been two bird strikes above 30,000 feet in North America in the last 5 years.