Most electrical outlets are designed for solid wire, you can buy the more expensive commercial receptacles that are made for stranded wire but you can terminate stranded wire on a residential receptacle using the method below.

Strip off about 3/4 of an inch of insultion.

Now using your wire strippers and strip another 1/8 to 1/4 of an inch of insulation but don't pull it all the way off, pull it out to the end of the bare wire and stop

Now wrap the wire around the screw on the receptacle and tighten down.

It is a good idea to wrap the electrical outlet with electrical tape before installing it into the box. This is a good practice with solid and stranded wire both.

This method of terminating stranded wire on electrical outlets has been used for ever by commercial electricians and is a great little trick to put in your bag.