Basically , Data in a Date column in Oracle can be stored in any user defined format or kept as default. It all depends on NLS parameter.
Current format can be seen by : SELECT SYSDATE FROM DUAL;
If you try to insert a record and insert statement is NOT in THIS format then it will give : ORA-01843 : not a valid month error. So first change the database date format before insert statements ( I am assuming you have bulk load of insert statements) and then execute insert script.
Format can be changed by : ALTER SESSION SET nls_date_format = 'mm/dd/yyyy hh24:mi:ss';
Also You can Change NLS settings from SQL Developer GUI , (Tools > preference> database > NLS)