Aircrew reported while transitioning Class D airspace to their destination ATC advised them of traffic and to expedite their descent. Aircrew reported traffic insight and was told frequency change approved. Aircrew reports while entering downwind they took evasive action to avoid the same traffic. The aircrew then continued to land without further incident.

Narrative

While descending northbound from 1;800 ft. MSL; Hillsboro Tower (HIO) received my request from 8 miles south to enter the Delta airspace 'Transition Approved' to land at OR81 and gave me the current altimeter setting 29.69.A short while later they issued a caution to the other aircraft (unknown operator) at 1;200 ft. MSL for my location ('Traffic 12 o'clock') and intended my flight path to our airport. HIO then gave me a directive to 'Expedite descent'. I pushed the nose further down; saw the other aircraft and determined my path was in front of and lower than the other traffic. I stated 'traffic in sight' and continued my approach and turn to our airport upwind pattern leg at 800 ft. MSL as per our operating procedure. HIO called me and directed 'Frequency change approved.' I changed frequency to our CTAF; announced my intentions and flew the 2;000 ft. length of our runway. Then I turned cross wind into downwind. Upon getting established on downwind; the other aircraft was less than a half mile; directly (1130-1200) ahead (estimated) 300 ft. higher and (estimated) less than 1;000 ft. laterally. I broke abruptly right and descended approximately an additional 100 ft.At our closing rate; the hazard only existed for a few seconds before it turned into a 'traffic no factor' situation. I continued my normal approach through base leg; into final and landed.What went wrong was Hillsboro Tower continued 2 aircraft into a possible collision course twice; the initial conflict and the near head-on in our established traffic area. HIO should have directed the other aircraft to clear our traffic pattern area by giving vectors away (south) from the area they knew was active. Hillsboro Tower should not have given me the clearance to change frequency. I should not have followed their direction to change frequency to our CTAF. I didn't know conflict still existed or could exist.What went right was the 'expedite descent' directive was issued quickly and clearly. Both aircraft missed collision. Twice.How to prevent this from recurring is that HIO needs to recognize the proximity of our airport within their Class D airspace. They need to modify their approach path to Runway 31 Left to have traffic enter their downwind pattern at a standard 45 degree entry abeam their tower or some other point to preclude traffic from routinely operating through our airspace.