I am going to assume that the little red and yellow lights you speak of are the running lights. Those are only powered through the electrical connection to the tow vehicle and only operate under that connection. They can be turned on with a special jumper that can be inserted to the trailer connector to the vehicle, but I assume you aren't using one of those. The porch and garage lights are powered by the battery when unconnected or inverter when connected to shore power. The 110V electrical outlets are completely different and only work when connected to shore power. Sounds like maybe lightning strike compromised the circuitry, burnt wires, blown fuses, and etc. in two separate circuits.
2011 Chevy 1500 SB 4x4 5.3L w/trailer tow
2013 Zinger ZT23FB
Reese Weight Dist. w/friction sway control