You can use TO_CHAR( date_value, 'D' ) to get the day-of-week.
However, this is dependent on the NLS_TERRITORY session parameter:
ALTER SESSION SET NLS_TERRITORY = 'AMERICA'; -- First day of week is Sunday
SELECT TO_CHAR( DATE '1970-01-01', 'D' ) FROM DUAL;
Outputs 5
ALTER SESSION SET ...