The ORDER BY clause is supported in recent versions of Oracle.
In your query I see a couple of problems. The first is if the T1.DATE_LAST_CALC column is of data type DATE, you'll get an error. In Oracle you have to convert to date before comparing. Secondly, you're trying to do 2 things here. Try putting brackets around the two dates your are subtracting.
OR '2015-06-01' - T1.DATE_LAST_CALC > 175
This should be close; if not, let me know:
CREATE OR REPLACE VIEW your_view AS
SELECT D1.DISTRICT_NAME, E1.EMP_FNAME, E1.EMP_LNAME, T1.TAX_YEAR, T1.DATE_LAST_CALC
FROM DISTRICT AS D1, EMPLOYEE AS E1, TOTAL_PAB AS T1
WHERE T1.DATE_LAST_CALC BETWEEN TO_DATE('2015-04-01', 'yyyy-mm-dd') AND TO_DATE('2015-04-04', 'yyyy-mm-dd')
OR (TO_DATE('2015-06-01', 'yyyy-mm-dd') - T1.DATE_LAST_CALC) > 175
ORDER BY DISTRICT_NAME, EMP_LNAME;