In neither North American nor UK English would "killed from the earthquake" be natural. I am not sure about Indian English. Nor would one say "killed from the storm" or indeed "killed from" in any construction. It might be logical, but it is simply not ever used, in my experience. Anyone saying this would be thought to speak English poorly.
Note this Google NGram which shows the usage of "killed from the" to be essentially zero in the Google English_2019 corpus, more than 100 times less frequent than "killed by the" or "killed in the".
Hundreds of people were killed by the earthquake
indicates that the earthquake was the actual cause of their deaths, but dies not distinguish between deaths directly caused by the earthquake (such as by people falling into a sinkhole), and deaths caused less directly by the quake, as by people crushed by falling buildings, burned by fires started during the quake, or trapped and dying of exposure, thirst, and so on. The same is true for other disasters such as "storm" or "explosion". Howevcer, where there is an active agency, the use of "by" tends to limit the statement to events caused directly by that agency.
Dozens of people were killed by the shooter.
would suggest that those people were actually shot and killed, and would not usually include, say, people dying of heart attacks or traffic accidents resulting from the shooting.
Hundreds of people were killed during the earthquake.
specifies the time period and not the cause. This sentence might include people dying from, say, lack of medical care, or even people killed by looters. Again the same applies to other causes such as "storm" or "riot".