What exactly are these unusual flight code names that require ATC priority?
NIGHT WATCH / NAOC

Night Watch or Nightwatch is the program identifier for the USAF National Airborne Operations Center (NAOC), including at least certain Boeing E-4 flights.

NAOC (used in flight):

From JO 7110.65W:


  The term “NAOC” will not be a part of the call sign but may
  be used when the aircraft is airborne to indicate a request
  for special handling.




FLYNET

From JO 7110.65W:  


  The code name “FLYNET” indicates that an aircraft is
  transporting a nuclear emergency team or a disaster
  control team to the location of a potential or actual nuclear
  accident or an accident involving chemical agents or
  hazardous materials. It is in the public interest that they
  reach their destination as rapidly as possible.




GARDEN PLOT

Classified. Related to operation Garden Plot. Presumably a callsign to be used by aircraft as part of that operation.



SCOOT

Term related to Special Air Mission flights in evacuation of government VIPs.

From JO 7110.65W:  


  The term “SCOOT” will not be part of the call sign but may
  be used when the aircraft is airborne to indicate a request
  for special handling.




OPEN SKIES

Callsign for observation aircraft under the Treaty on Open Skies. The USAF aircraft used for this purpose is the OC-135.

From Wikipedia's Treaty on Open Skies:  


  Observation/Demonstration flights are conducted
  under rigid guidelines outlined in the Treaty of OPEN
  SKIES that govern sensor usage, maximum flight
  distances, altitudes and priorities.