The purpose of stranded is Flexibility. It is more expensive than solid, thats why solid is used in home wiring. In the industrial setting, I allways use stranded wire of some form. Just remember, you need a Sta-Kon, preferably the fork style to affix the wire to the duplex receptical. the stranded does not stay under the screw that well and could come out, causing a short. Heres a pic, although, for 14AWG, you will want blue colored ones. Yellow is for 12AWG, and red is for 18-16AWG
Now, the extension cord ends, they are made for stranded. The screw has a metal piece with it, that acctually clamps the wire, so no need to worry about the Sta-Kon's with cord ends.