What is the proper method of wiring outlets on the basement wall. The wall has 2x3 firring strips 16" OC. Does the wire have to be in conduit?

Typically, with 2" x 3" studs, I assumed laid flat, 4 inch square boxes 1-1/2" deep with side brackets are mouthed to the side of the stud, and raised mud rings that match the depth of the drywall, are used. Being a basement, we would normally run up the stud to the ceiling to run the cable horizontally to drop down to the next box, and so on.

If you drill through the studs, each stud the cable crosses will need a protective steel plate covering the path of the cable.