Oracle SQL – DATE greater than statement

As your query string is a literal, and assuming your dates are properly stored as DATE you should use date literals:

SELECT * FROM OrderArchive
WHERE OrderDate <= DATE '2015-12-31'

If you want to use TO_DATE (because, for example, your query value is not a literal), I suggest you to explicitly set the NLS_DATE_LANGUAGE parameter as you are using US abbreviated month names. That way, it won’t break on some localized Oracle Installation:

SELECT * FROM OrderArchive
WHERE OrderDate <= to_date('31 Dec 2014', 'DD MON YYYY',
                           'NLS_DATE_LANGUAGE = American');