select
  'null columns: ' ||
  case when max(col1) is null then 'col1 ' else '' end ||
  case when max(col2) is null then 'col2 ' else '' end ||
  case when max(col3) is null then 'col3 ' else '' end ||
  case when max(col4) is null then 'col4 ' else '' end ||
  ...
from mytable;

DECLARE @strTablename  varchar(100) = 'dbo.MyTable'
DECLARE @strQuery  varchar(max) = ''
DECLARE @strUnPivot as varchar(max) = ' UNPIVOT ([Count] for [Column] IN ('

CREATE TABLE ##tblTemp([Column] varchar(50), [Count]  Int)

SELECT @strQuery = ISNULL(@strQuery,'') + 'Count([' + name + ']) as [' + name + ']  ,' from sys.columns where object_id = object_id(@strTablename) and is_nullable = 1
SELECT @strUnPivot = ISNULL(@strUnPivot,'') + '[' + name + '] ,' from sys.columns where object_id = object_id(@strTablename) and is_nullable = 1


SET @strQuery = 'SELECT [Column],[Count] FROM ( SELECT ' + SUBSTRING(@strQuery,1,LEN(@strQuery) - 1) + ' FROM ' + @strTablename + ') AS p ' + SUBSTRING(@strUnPivot,1,LEN(@strUnPivot) - 1) + ')) AS unpvt '

INSERT INTO ##tblTemp EXEC (@strQuery)

SELECT [Column] from ##tblTemp Where [Count] =0

DROP TABLE ##tblTemp