Run the following query:

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SELECT parameter, VALUE  
FROM nls_database_parameters  
WHERE parameter IN (  
  'NLS_CHARACTERSET',  
  'NLS_NCHAR_CHARACTERSET',  
  'NLS_TERRITORY',  
  'NLS_LANGUAGE',  
  'NLS_SORT'  
)  
ORDER BY parameter;

Typical output will be something like this:

PARAMETER               VALUE
----------------------  ---------
NLS_CHARACTERSET        AL32UTF8   
NLS_LANGUAGE            AMERICAN   
NLS_NCHAR_CHARACTERSET  AL16UTF16  
NLS_SORT                BINARY     
NLS_TERRITORY           AMERICA

NLS_LANG, which summarizes the above settings, will look something like this:

NLS_LANG=american_america.AL32UTF8