Try this -
DECLARE @table VARCHAR(100) = 'dbo.table'
DECLARE @sql NVARCHAR(MAX) = ''
SELECT @sql = @sql + 'IF NOT EXISTS(SELECT 1 FROM ' + @table + ' WHERE ' + c.name + ' IS NOT NULL) PRINT ''' + c.name + ''''
FROM sys.objects o
JOIN sys.columns c ON o.[object_id] = c.[object_id]
WHERE o.[type] = 'U'
AND o.[object_id] = OBJECT_ID(@table)
AND c.is_nullable = 1
EXEC(@sql)