PIPER INSTRUCTOR PLT HAS NMAC WITH C150 DURING PATTERN ENTRY AT A CTLED ARPT.

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I WAS THE FLT INSTRUCTOR (R SEAT) IN A PA23-150 DURING A VFR MULTI-ENG TRAINING FLT. WE APCHED KALAELOA ARPT FROM THE NE AT 1000 FT; 110 KTS. AFTER CONTACTING THE TWR; WE RECEIVED INSTRUCTIONS TO ENTER A L DOWNWIND FOR RWY 4L. NO OTHER TFC INFO WAS GIVEN; HOWEVER; IT WAS APPARENT 2-3 OTHER ACFT WERE OPERATING IN THE TFC PATTERN FOR RWY 4L&R. THE STUDENT DSNDED TO 800 FT MSL AND SLOWED TO 100 KTS. THE CTLR WAS HAVING DIFFICULTY DETERMINING THE CALL SIGNS AND POS OF 2 ACFT WITH SIMILAR SOUNDING CALL SIGNS. AS OUR ACFT ENTERED THE L DOWNWIND; THE CTLR SAID 'N-NUMBER; ACFT Y; YOUR TFC IS TURNING L DOWNWIND ABEAM THE DEP END OF RWY 4L.' I REALIZED THAT WAS OUR EXACT LOCATION. I SEARCHED TO OUR 10-11 O'CLOCK POS; UNABLE TO FIND THE TFC. AS I TURNED TO MY 8-9 O'CLOCK POS; I SAW A C150 SLIGHTLY BELOW AND HDG DIRECTLY TOWARD MY L WING. I DIDN'T EVEN HAVE TIME TO ACKNOWLEDGE THE CTLR; BUT I TOOK THE AIRPLANE; BANKED 60 DEGS; ADDED FULL PWR AND TURNED DIRECTLY DOWNWIND. I AVERTED THE COLLISION; HOWEVER; THE ACFT WAS NOT MORE THAN 200 FT HORIZ AND NOT LESS THAN 25 FT VERT FROM MY POS. I CONTINUED FLYING THE DOWNWIND; RPTED TURNING BASE; AND NOTICED THE C150 STARTED TO TURN ITS BASE (UNTIL THE PLT NOTICED US ON BASE). THE C150 THEN CONTINUED ON THE DOWNWIND. AFTER I RPTED BASE; THE CTLR ASKED WHO RPTED BASE. CLRLY THE (AIR NAT GUARD) CTLR WAS OVERWHELMED WITH THE 4 ACFT OPERATING ON 2 RWYS. AFTER OUR LNDG; WE DEPARTED UNEVENTFULLY.