Use the junction box that attaches right to the conduit; the conduit should run right into the crawl space into the box. Although solid is preferred because it has less resistance, you will be OK with the stranded for the small amount of current you will draw at that appliance.
So this is the outlet I want to change to a j box, if it’s plastic should I replace with metal and use the wire clamps to and from and convert to single wires and conduit in crawl space? This outlet is about 10 ft from the crawl space access and where I want to install the new outlet outside. Not too worried about this slate tile being damaged as the bathroom needs to be redone soon.
Interesting, would be what was there, in that area, to have resulted in the recep. being there.
If the power for that recep. originates from the underfloor area, as if it had originally been power for an elec. wall heater, abandon it and "J" box to the floor joist and continue from there with either romex or flex. If it originates in the attic then either raise it to counter height and install a GFCI, or raise it to 15-1/2"
above the finished floor and turn it 180 degrees to make it accessible from the opposing wall.