PIPER PA-31, N200GG, WAS ON A VFR FLT TO BOSTON, MA. THE PA-31 PLT CONTACTED BOSTON TRACON & ADZD HE HAD ATIS INFO & WOULD BE LNDG AT BOSTON. TRACON SUGGESTED A HDG & ALT OF 070 DEG & 2500' FOR RWY 33R & TOLD THE PLT TO MAINT VFR. AT APRX THE SAME TIME, A STUDENT & INSTRUCTOR (CFI) WERE ON A LCL INSTRUMENT TRAINING FLT IN THE AREA. THE STUDENT WAS IN THE L SEAT, WEARING A VIEW LIMITING DEVICE. THE 2 ACFT CONVERGED IN VFR WX & COLLIDED AT APRX 2600'. THE PA-31 WAS ON A NE HDG; THE CESSNA WAS ON A NW HDG. DRG IMPACT, THE TOP OF THE PA-31'S VERTICAL STABILIZER HIT THE LWR LEFT SIDE OF THE CESSNA'S FUSELAGE, INJURING THE STUDENT'S L LEG & DAMAGING THE CESSNA'S RGT MAIN GEAR. BOTH ACFT LNDD SAFELY, EXCEPT THECESSNA SWERVED OFF THE RWY DRG THE LNDG ROLL. THE PA-31 WAS SQUAWKING CODE 4640 WITH MODE C (ALT RPRTG). THE CESSNA WAS TRANSPONDER EQUIPPED, BUT DID NOT HAVE MODE C CAPABILITY. ITS TRANSPONDER WAS SET AT 1200, BUT WAS ACTUALLY SQUAWKING 1270. THE RADAR CTLR WAS UNABLE TO IDENTIFY THE CESSNA AS POTENTIAL CONFLICT. NO RADIO CONTACT BTN THE CESSNA & TRACON.