turning my system on during lightning storms

Grounding antena won't protect from direct hit (even ground rod is problematic). The real purpose for grounding antena is to prevent static electricity build-up caused by the wind that can charge your antena to several kV making it electrically the "tallest" structure in the area. Size of the grounding wire does not matter.

Always unplug to prevent ground differentials.

Lightning never strucks GPX - it always chooses the most expensive system in the area!

Direct lightning creates plasma about 1 foot in diameter and there is no wire in the world to bring it to ground, but if it gets one of the smaller "branches" it might protect as long as wire is thick and does not have sharp angles (short time = high frequency). I have tall street lamps around my house working as grounding rods. Not grounded antena migh appear taller than street lights (or trees).

Timhru - I experienced horrible thunderstorm in the mountains when I was young. I remember people closing windows and talking about plasma/fire ball that can move horizontally and come thru the window - scary.

Current will find all possible paths to ground even if your tuner provides easy one. When the rest of equipment is unplugged and well isolated from the ground current won't flow thru it but will flow thru center wire of your interconnect to input of an amp and back (high voltage will destroy/short input) thru interconnects ground to tuner and earth ground. This is not very "efficient path" but your amp's input doesn't need much to get damaged. Unplug everything.

Tonywinsc - your damage of three prong devices suggest that lightning hiting tree/ground near the house creates big voltage differential between earth ground and neutral wires. Switching off equipment would not help since switch is on the hot wire. Recently I looked at power strips in Tiger.com store and the most expensive one not only had the most of Joules but also different split betweens tree lines. It had acually less Joules than cheaper one on the hot wire and much more between ground and neutral.

Tonywins - I have to fine my receipt and save it. There was warranty as well but I did not treat it seriously. Thanks for the info.