United Flight 97 experienced indications of uneven fuel flow from main tanks 2 and 3 at FL360 beginning about 4 hours after departure on an 11-hour transpacific flight. The fuel system had been set up for all engine feed from the Nos 2 and 3 tanks. Although it was later established that the number 2 crossfeed valve failed in the closed position, the S/O informed the Capt that the intransit light had illuminated when the valve selector was moved to the closed position - indicating normal crossfeed valve operation. Fuel system problem was misdiagnosed as a problem of faulty fuel gage indications. Fuel monitoring indicated insufficient fuel flow from No 2 tank when crossfeeding. Engines 1, 3, and 4 flamed out when fuel was expended from all tanks except No 2. Emergency descent was made to destination Tokyo-Narita Airport. Crew reported they used flaps-20, but DFDR showed flaps-1 was used for landing. Three tires blew on landing. All 3 flightcrew qualified in the B-747 in the 13-months before the incident.