I have heard of violently pulsating solar flares during times of extreme Sun Spot activity, while the Earth is entering, in, or exiting Solar Convergence [the Equinoxes] doing this - last known large event was early 1990's in eastern Canada. Knocked out the entire Power Grid for a week.
Makes sense if this occured in late March, thru early May, or late August thru early October [Equinox periods].
Now as far as the stories from listeners goes, nearly all of them are going to be biased towards the supernatural and unexplainable - which dillutes the persons' interpretation of the events they witness primarily from a mild state of shock, or just feeling that it's got to be alien! [sorry for the Psych 101
The nuke plant would have stainless steel tanker trucks coming and going here and there, as normal operating procedures. Likely they are bringing in Heavy water, which is used as a Moderator on a Fission Reaction.
The trucks could have also been carrying unused U238 fuel, or removing the used U239 saturated U238 fuel.
The guy with the Fluorescent lamp lighting is not so strange. On a dry, slightly windy day, wear some rubber soled shoes, then rub your feet on a freshly swept carpet. Grab a Fluorescent lamp and it will flash on at about 10% full brightness, then decay semi rapidly to a faint glowing state.
You could even hold the lamp and rub your feet, which will do about the same thing.
For the humming noises, seems most likely to be machinery / fans / etc. in the distance, which the sound is being reflected just right due to relative humitity, clouds and mild winds.
I have heard some really strange and funny stuff coming from Disneyland at 1:00-2:00 in the morning, which is when the techs do level sets and such.
Can't explain the Helecopters - maybe they just do not want people having unauthorized access to a Nuclear Fascility??? Imagine that!
The illnesses could be attributed to ground water poisioning [such as Cromium-6 on "Erin Brokovich"], or even underground high voltage transmission feeders in close proximity.
Don't get me wrong here!! I have a great interest in extraterestrial items and have been an loyal X-Files watcher [until the last season when Mulder came and went, then came, then went, then came, then went, then came, then