B757 FLT CREW HAS A TRACK HDG DEV DURING DEP FROM ZSPD.

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DURING TAXI AND ON THE RWY AT PVG ALL SYS AND INDICATIONS WERE NORMAL. SPECIFICALLY; THE MAP DISPLAY SHOWED THE RWY IN PROPER ALIGNMENT WITH THE ACFT AS WE TAXIED OUT AND LINED UP FOR TKOF. IN ADDITION; THE MAGENTA RTE LINE WAS POSITIONED CORRECTLY. AT LIFTOFF WE RECEIVED A GPWS WARNINGS: 'TOO LOW; TERRAIN.' AT 400 FT AND 1000 FT RESPECTIVELY WE ENGAGED LNAV AND VNAV; AND APPEARED TO TRACK OUR COURSE NORMALLY. AFTER AN APPROX 90 DEG L TURN FROM RWY HDG; WE WERE EXPECTING ANOTHER L TURN ON COURSE TO TAO AND WERE CLRED TO PROCEED DIRECT TO PINOT INTXN. ACCORDING TO THE FMC; THIS WOULD BE A R TURN AWAY FROM TAO. WE QUERIED DEP CTL; ASKING 'CLRED FOR A R TURN DIRECT PERNOT?' ATC DID NOT CHANGE THE CLRNC. WE BEGAN THE TURN AND ASKED FOR OUR ROUTING AFTER PERNOT BECAUSE FMC WAS SHOWING A 180 DEG COURSE REVERSAL AT PINOT TO PROCEED TO THE NEXT FIX; ODULO. THIS DID NOT MAKE SENSE. WE WERE TOLD THAT ODULO WAS IN FACT THE NEXT FIX; SO WE ASKED ATC TO SPELL PINOT. THEY DID; CONFIRMING WE HAD THE CORRECT INTXN ENTERED IN THE FMC. AT THAT TIME ATC SAW WE WERE TURNING R AND CALLED AND TOLD US TO TURN L FOR DIRECT TO PINOT. WE TOLD PVG CTL WE WERE UNABLE DIRECT PINOT; AND THAT WE WERE NO LONGER RNAV EQUIPPED; AND WERE GIVEN VECTORS ON COURSE. WE THEN DISCOVERED THAT WE HAD A 30+ NM DISPARITY BTWN THE FMC POS AND THE GPS POS WHICH WAS DISPLAYED ON THE ADSB MENU PAGE. IT APPEARED THAT THE GPS POS WAS THE MORE CORRECT POS. THE 30+ NM DISPARITY CONTINUED FOR THE REMAINDER OF THE FLT WHICH WE CONDUCTED USING RADAR VECTORS AND RAW DATA.