It doesn't matter whether the device is on or off because the surge is large enough to put across any small switch or even through the ground side.  Who knows, but only being unplugged and that includes the modem or lan card, will really help you or a surge protector.

I had an old TV that wasn't on that got zapped by lightnining some years ago.  I opened it up and saw an inline fuse had been melted.  I bypassed the fuse just to see if I could get it to work and it was a big NO.  It was fried.

PatD, you might be able to recover your data from your drives though.

But, surge protectors do help.

I have a surge protector into the wall and an APC UPS battery/surge protector plugged into that.  I can't tell you how nice it is to have battery power to keep you going when the power stops.  You can UPSs for well under $60 USD.