What is the night of Islamic event like Shab e Meraj e.g on 3rd April 2019 it is Shab e Meraj but some people say it is the night before that is to be worshipped I.e. 2nd April.
Same like 27th of Ramadan. People worship on 26th evening/night.
What are sources of it?
The days in the Islamic calendar don't start at midnight like our modern Gregorian calendar days do, rather, the new day is considered to start at sunset (i.e. maghrib time). Therefore days on the Islamic calendar won't perfectly match up with the days on a modern calendar, and would typically include the previous night as in the examples you listed.
