Can stranded wire be used for pigtails in a junction box?
As long as all the equipment is listed for the use, there's no problem using stranded wire. The UL White Book says that screw terminals and pressure plate terminals can be used with both solid and stranded wire.


  UL White Book 2013
  
  Receptacles(RTDV)
  
  Receptacles for Plugs and Attachment Plugs (RTRT)
  
  Terminals
  Terminals of the wire-binding screw, setscrew, or screw-actuated backwired
  clamping types are suitable for use with both solid and stranded
  building wires.


It says switches are solid only, however, you can use terminal connectors such as fork connectors.


  Switches (WFXV)
  
  Snap Switches (WJQR)
  
  Terminals
  Terminals of the wire-binding screw, setscrew, or screw-actuated backwired
  clamping types are suitable for use with solid building wires unless
  otherwise indicated either on the device or in the installation instructions.
  
  Terminals of a flush snap switch are permitted for use with Listed field-installed
  crimped-on wire connectors or an assembly, if so identified by
  the manufacturer.
  
  A flush snap switch may also be provided with conductor leads with
  factory-installed crimped-on connectors. Such connectors may be either
  attached to the flush snap switch terminal or are provided with the flush
  snap switch in the smallest unit shipping container and are suitable for
  use with the terminal of the flush snap switch.


Wire connectors (including twist-on wire connectors) can be used for both solid and stranded wire sizes between 30-10 AWG, in combinations listed by the manufacturer. Unless they are clearly marked to be used with one type or the other.


  Wire Connectors (ZMKQ)
  
  Wire Connectors and Soldering Lugs (ZMVV)
  
  Wire stranding -- Unless clearly marked "Solid," "SOL," "Stranded" or
  "STR" for a given wire size, wire range or wire combination, conductors in the range 30-10 AWG are both solid and stranded, and 8 AWG and larger
  are for stranded wire only.


Ideal Industries has a handy PDF, that lists all the allowable wire combinations that can be used with their various connectors. For example, the Ideal 74B® (their basic yellow wire-nut) can be used with 1 - 4 #14 solid or stranded conductors.