B747 HAS RWY INCURSION DURING TAXI IN DURING A NIGHT OP AT ORD.

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ACFT LANDED AT ORD ON DEC/SUN/02. LNDG RWY 27R; VISIBILITY 10 KM; WIND 220 DEGS AT 17 KTS. THE ACFT WAS 225000 KG. WE ACCEPTED THE VISUAL APCH WITH THE ILS BACK-UP. TFC WAS EXTREMELY HVY WITH MULTIPLE RWY USAGE. WE EXITED THE RWY AT TXWY E AND HELD SHORT OF RWY 22R ON TXWY E. WE WERE THEN CLRED TO CROSS RWY 22R ON TXWY E AND MAKE A L ON TXWY A AND CONTACT GND CTL. GND CTL CLRED US ON TXWY A; R ON TXWY H AND HOLD SHORT OF RWY 32R ON TXWY H3. AS WE PROGRESSED SLOWLY; #3 FUEL FLOW WAS FLUCTUATING WILDLY AND I TOLD THE FE TO SHUT IT DOWN. THIS WAS ACCOMPLISHED -- ALL THE WHILE GND CTL WAS GIVING NEW INSTRUCTIONS. ORD GND NEXT INSTRUCTED US TO MAKE A R ON TXWY P AND HOLD SHORT OF RWY 32R. WE WERE STILL MOVING WHEN GND INSTRUCTED US TO MAKE THE NEXT L; WHICH IS TXWY A; AND HOLD SHORT OF RWY 27R. AGAIN; WHILE STILL MOVING. WE WERE INSTRUCTED TO KEEP IT ROLLING AND CROSS RWY 27R. WHEN WE WERE INSTRUCTED TO MAKE THE 'NEXT L' I RESPONDED BY SAYING 'ROGER; L TURN HERE AT TXWY A; SHORT OF RWY 27R.' THE L AT TXWY A HAD PLACED US ON TXWY H2. WHEN WE WERE TOLD TO KEEP IT MOVING AND CROSS RWY 27R; WE MUST MAKE A R TURN ON THE RWY AND A QUICK L ONTO TXWY V2. AS WE WERE PERFORMING THIS MANEUVER ON RWY 27R; THE CTLR ASKED US WHAT WE ARE DOING; I RESPONDED THAT I HAD NOWHERE TO GO; BUT THIS DIRECTION. XING RWY 27R AT TXWY H2 WOULD HAVE PUT US INTO THE GRASS IF WE CONTINUED STRAIGHT. ANOTHER JET ON FINAL WAS INSTRUCTED TO GO AROUND EVEN AS WE ENTERED TXWY V2. IN MY JUDGEMENT; HE WAS NOT CLOSE; POSSIBLY BTWN 1/2 MI AND 3/4 MI. AFTER THE INCIDENT AND OUR ENSUING TAXI TO THE PARKING AREA; WE HAD NO FURTHER DIALOGUE WITH THE ORD CTLR. WE REMAINED ON FREQ UNTIL THE ACFT WAS PARKED AND THE ENGS WERE SHUT DOWN. SUPPLEMENTAL INFO FROM ACN 567291: CONDITIONS WERE DARK AND TFC WAS HVY. I (THE FO) WAS TAXIING THE ACFT. GND THEN INQUIRED WHY WE HAD TURNED ONTO THE RWY AS THERE WAS AN ACFT ON FINAL APCH. CAPT RESPONDED BY SAYING 'THERE IS NOWHERE ELSE TO GO AND WE ARE EXPEDITING!'