I'd like to know if this can be done safely. If I have a 12/3 extension cord plugged into a covered outdoor outlet, can I wire the other end into a (new) switched outlet? (the length would be about six feet) I know stranded wire is not the preferred type, but I have a tight area in which to work. Proposed outlet is a GE 20A backyard version. (please, no gasping, I haven't done anything yet)
There's no problem with using stranded wire, as long as it's properly sized. The problem with your plan, is that you want to use an extension cord.
An extension cord is meant to be used as a temporary wiring method, with the cord intact and undamaged. Once you cut the end off the cord, the cord is no longer UL listed, and cannot be used in a code compliant manner.
You can use any cable or wire that is listed for wet/outdoor locations, whether it be solid or stranded wires. Underground Feeder (type UF) cable is a common choice, if you want to use cable. If you choose to use cable, you'll have to make sure that it's protected from physical damage.
THWN wire would be acceptable, if you want to run it through conduit.
Nobody should tell you it is safe. Will it work, yes. Is it dangerous, very.
I have ran wiring through the tightest spaces with many turns all underground, no camera, under concrete with steel fish tape (similar to snake lines) when building car washes).
You need to just get some romex, conduits and run it up to code. Safety first :)
If you really want to use the extension cord, then simply plug 1 thing into at the end, while plugged into the wall.