Computers draw power when turned off, to keep the clock running. Notebooks pull power for battery charging, all the time. Monitors have fancy ‘soft switches’, which electronically sense a finger press. Pure mechanical switches will actually cut power, but most electronics don’t have them. The front switch on a tower is what we call a ‘momentary contact, single-pole’ switch–it just sends a signal to the mainboard to turn on or off, and doesn’t isolate anything. So turning off a computer isn’t enough. You have to disconnect it from power completely.
How? Quickest way is to flip the small rocker switch on the surge suppressor strip; that should take care of everything that connects to the computer at once. For notebooks, unplug the charger, it’s time to go cord-free.
Same thing applies to all electronics, not just computers. Anything that uses a remote control is connected to AC power, and turned on, at least at a low-power level–unplug it before the lightning reaches your area.
And finally: Remember to also unplug the network cable–half the lightning strike repairs I fix here in Maryland are from a lightning strike at the power pole carrying the Internet into the router, which continues into the network and burns out computers.