AN ACR WDB FREIGHTER FLC DEPARTS FROM THEIR CLRED RTE WHEN THEY ENTER THE WRONG RTE INTO THE FMS. THE ARTCC RADAR CTLR CORRECTED THEM BACK TO COURSE.

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ATC CLRNC WAS VIA 'APU 1' SID W7/B591 DIRECT FPR FL310. I HAD THE FO LOAD THE ROUTING IN FMS DUE TO DOING IOE (FL). HE ASKED ABOUT ANTICIPATED DEP AND I SAID USE THE ANPU 1/5L WITH THE WADER TRANSITION. WHEN WAYPOINTS WERE CHKED 'TINHO' AND GID VOR DIDN'T SHOW UP IN THE STANDBY FLT PLAN; BUT I MISTAKENLY SAID LET'S GO THROUGH THE REST AND WE'LL CHK IT IN THE ACTIVE FLT PLAN. DUE TO SOME LAST MIN BUSY TASKS; I FAILED TO HAVE THE ROUTING VERIFIED AGAIN. WE TOOK OFF ON RWY 5L ANPU 1 SID AND PROCEEDED VIA FMS NAV APU VOR; 154 DEG RADIAL OUTBOUND. APPARENTLY THE FMS HAD DIRECT HCN VOR FROM WADER INTXN INSTEAD OF W7 TINHO AND W7 OVER GID TO HCN VOR. TAIPEI CTL SAID WHAT I THOUGHT WAS 'YOU'RE 4 MI L OF COURSE;' SO I SAID; 'LET'S TURN R A LITTLE AND VERIFY THE ROUTING.' I PUT IN ABOUT A 20 DEG HDG TO R TEMPORARILY. WHILE WE WERE DISCUSSING WHAT WAS NEEDED TO CORRECT THE FMS THE CTLR THEN SAID WE WERE '10 MI W OF COURSE.' AT THAT TIME WE TURNED BACK TO THE L AND EITHER ASKED FOR OR RECEIVED A HDG (NOT SURE) THEN ATC CLRED US DIRECT TO GID VOR WHICH IS ON W7. AT THAT POINT I REALIZED THAT THE ACFT HAD CROSSED WADER AND TURNED DIRECT TO HCN VOR. WE HAD NOT LOADED THE W7 AIRWAY FROM WADER TO HCN VOR WHICH WOULD HAVE PROCEEDED OVER TINHO DIRECT GID DIRECT HCN. AS THE SAYING GOES 'GARBAGE IN; GARBAGE OUT' AND THE WORST THING IS THAT I HAD THE OPPORTUNITY TO MAKE SURE THE ROUTING WAS CORRECT WHILE STILL IN THE BLOCKS PRIOR TO ENG START AND I DON'T KNOW WHY I DIDN'T. USUALLY I'M DOUBLE CAUTIOUS ON THE THINGS; BUT SOMEHOW IN THIS CASE IT MANAGED TO SLIP BY ME. IT'S MY RESPONSIBILITY TO CHK REGARDLESS OF THE DUTIES ASSIGNED THE NEW FO. VERIFYING THE ROUTING IS PARAMOUNT AND WILL BE IN THE FUTURE.