Sorry to hear about all the damage
Ok, a time varying electromagnetic field can induce current in a nearby conductor. That is how AC motors and transformers work. Even far away EM sources can induce small current hence we have broadcast radio, TV and cell phones. A current is induced in the receiving antenna, amplified and the information is recovered. Wireless communication as they say.
A lightning strike is a time varying EM field of huge proportions, very intense and capable on inducing a very large flow of current in any nearby conductors. A strike far away may send a surge down the power lines and cable lines and surge protectors may protect your electronics. What about a nearby strike?
A strike near your house can induce very large current in any conductive material. House wiring for electric or cable are good antennas and an underground dog fence is a perfect antenna as well as wiring to a driveway gate. This kind of surge does not come in via power lines but is induced or generated right within the local conductive wiring. Little or nothing can be done to stop it.
http://www.sto-p.com/pfp/pfp-iemf.htm
Alan