A B757 PILOT REPORTS CABIN ELECTRICAL FUMES AFTER A 'STBY INVERTER' EICAS MSG. THE SMOKE AND FUME CHECKLIST WAS COMPLETED AND THE FUMES DISSIPATED.

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WE WERE CRUISING AT FL340 AND GOT A STATUS MESSAGE OF STANDBY INVERTER. 3-4 MINS AFTER WE GOT THE MESSAGE; WE STARTED GETTING CALLS FROM THE PAX CABIN STATING THAT THERE WAS THE DISTINCT ODOR OF BURNING PLASTIC. THE ODOR WAS RPTED INITIALLY IN THE BACK OF FIRST CLASS CABIN AND WITHIN A COUPLE OF MINS IT HAD SPREAD TO THE AFT CABIN BY DOORS 3L AND R. THE CAPT CONTACTED A COMPANY B767 WITH SATCOM TO FORWARD OUR INFO TO DISPATCH AND MAINT. I PULLED OUT THE QRC SMOKE/FUMES/ODOR CHKLIST AND PROCEEDED TO RUN THE CHKLIST. WE NEVER HAD ANY ODOR IN THE COCKPIT AND THEREFORE WE DID NOT DON OXYGEN MASKS OR SMOKE GOGGLES. AFTER RUNNING THE QRC AND RELATED PROC IN THE FM; THE ODOR DID DISSIPATE FROM THE CABIN. WE HAD A DEADHEADING B767 PLT IN FIRST CLASS. I TALKED TO HIM AND RELATED THE SITUATION. HE WALKED THROUGH THE CABIN AND RPTED HIS FINDINGS TO US. WE ESTABLISHED AN HF PATCH WITH DISPATCH; MAINT AND THE DUTY MGR. WE SPENT APPROX 45 MINS TALKING TO THESE 3 RESOURCES AND DETERMINED TOGETHER THAT THE BEST DECISION WOULD BE TO PROCEED TO ZZZ1. WE WERE TOLD THAT THE ZZZ2 STATION PERSONNEL WOULD REMAIN AT THE ARPT UNTIL WE LANDED IN ZZZ1 IN CASE WE NEEDED TO DIVERT. THE CAPT AND I DISCUSSED HAVING THE FLT ATTENDANTS DO A CABIN ADVISORY. WE DECIDED TO HAVE THEM DO THAT. THE FLT ATTENDANTS REQUESTED THAT WE PUT THE UTILITY BUSES BACK ONLINE SO THAT THEY WOULD HAVE CABIN LIGHTS. THE CAPT AND I DISCUSSED THAT AND OPTED TO LEAVE THEM OFF AS WE WERE STILL AN HR FROM THE CLOSEST ARPT IN CASE THAT WAS THE CAUSE OF THE ODOR. WE DECIDED THAT ONCE AT THE GATE; WE WOULD PUT THE UTILITY BUSSES ONLINE FOR PAX DEPLANING. THE REST OF THE FLT WAS UNEVENTFUL. WE LANDED IN ZZZ1 AND TAXIED TO THE GATE. I THINK THAT THE CAPT DID AN EXCELLENT JOB MANAGING THE SITUATION. WE HAD VERY GOOD RESOURCES ON THE ACFT INCLUDING THE FLT ATTENDANTS AND THE DEADHEAD PLT. ALL RESOURCES ON THE GND; DISPATCH; MAINT; AND THE DUTY MGR WERE READILY AVAILABLE; AS WERE THE GND STAFF IF WE NEEDED THEM. WE OPTED NOT TO DECLARE AN EMER AS THE ODOR WAS ELIMINATED BY RUNNING THE QRC. I THINK THAT WAS A REASONABLE DECISION.