I had two thin (maybe 10 or 12 gauge) over head electrical wires running from the house to the garage, each was a single wire. These wires powered were two outside lights (so I could turn them on from the house). The wires were wrapped/tied to insulators on the house and garage.

A storm came through the area, and the wires were downed, so now I need to replace them. The electrical supply companies in my area only sell a 6 gauge or heavier multi-wire wire.

What do I use to replace these 30-yr-old wires and where can I purchase it?

Assuming a 30 amp or less feeder, you may use #10-2 with ground UF cable, no longer than 50 foot span between buildings.

Need to check local codes, here in Maine we must use a messenger cable to support overhead cables, no matter the span distance.

Best would be to use 1/8 inch steel messenger cable (aircraft cable) and tyrap the UF cable to the messenger, every 12 inches, using UV rated tyraps. White or clear tyraps usually are not UV rated, black tyrpas usually are UV rated.

UV = sunlight resistant.