B767 CREW HAD ELECTRICAL SMOKE AND FUMES IN THE COCKPIT AND CABIN.

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CABIN SMOKE/COCKPIT SMOKE. WHILE CRUISING AT FL350 FROM GRU TO JFK; I THOUGHT I COULD SMELL SMOKE IN THE COCKPIT. AFTER VERIFYING THIS WITH THE OTHER PLT; I AWAKENED THE CAPT; ON BRAKE; TO ASSIST IN THE MATTER. HE CAME TO THE COCKPIT IMMEDIATELY. WE QUICKLY EVALUATED THE SIT; DETERMINED WHERE THE NEAREST SUITABLE ARPT WAS; AND DIVERTED. I FLEW THE ACFT WHILE THE CAPT AND THE OTHER PLT RAN APPROPRIATE CHKLISTS. AFTER LNDG; WE PERFORMED AN EMER EVAC BY USING THE ESCAPE SLIDES. SUPPLEMENTAL INFO FROM ACN 501889: APPROX 6 HRS INTO FLT FROM BGR TO JFK; FO AND MYSELF NOTICED FUMES; THEN SMOKE; IN COCKPIT. FO WENT TO WAKE CAPT. UPON THEIR RETURN; THEY NOTICED FUMES/SMOKE IN FIRST CLASS -- LOWER EICAS DISPLAYED 'SBY INV.' WE ASKED FOR AND RECEIVED IMMEDIATE TURN/DSCNT TO CURACAO. CAPT REPLACED ME IN L SEAT. WE THEN DONNED OXYGEN MASKS AND SMOKE GOGGLES. WE ACCOMPLISHED CABIN FIRE/SMOKE; CABIN /COCKPIT SMOKE REMOVAL; AND BEGAN ELECTRICAL FIRE OR SMOKE PROCS. THIS WAS INTERRUPTED IN LIEU OF THE BEFORE LNDG CHKLIST. WX AT CUR CLR SKIES; WIND 10 KTS FROM W. FO ACCOMPLISHED VISUAL RWY 27. AFTER LNDG; FLT ATTENDANTS RPTED SMOKE THICKENING AND BURNING PAX'S EYES. CAPT DECIDED TO EVAC. RAN GND EVAC CHKLIST AND EVACED WITHOUT INCIDENT.