A B737-300 CREW FAILED TO CHK THE ROUTING AND ACCEPTED AN ILLOGICAL DEP CLRNC THEN MISSED A DIRECT CLRNC VACATING THE ORIGINAL ILLOGICAL CLRNC. FATIGUE MAY BE A FACTOR.

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WE WERE FLYING A B737-300 AND IT WAS THE LAST LEG OF A 4-DAY TRIP. WE HAD BEEN REROUTED DUE TO A MECHANICAL PROB ON DAY 2; AND IT RESULTED IN THE LAST LEG HAVING A SHOWTIME OF XA:15; WITH A 12+ HOUR DUTY DAY. WE HAD A 9:50 RON AND I TRIED TO GET TO SLEEP EARLY; BUT ENDED UP ONLY GETTING ABOUT 4-5 HOURS OF SLEEP. WE DEADHEADED TO JAX AND THEN FLEW JAX TO ANOTHER CITY; THEN OUR FINAL DEST. AFTER COMPLETING THE CHKLIST FOR THE FINAL LEG; MY FO BRIEFED THE RTE; AND I CHKED THE ROUTING ON THE FMC. THE RTE MATCHED; HOWEVER; I FAILED TO CATCH THAT IT DIDN'T MAKE A WHOLE LOT OF SENSE. I AM NOT SURE WHERE THE ERROR HAPPENED; BUT THERE WAS A MISCOMMUNICATION WHEN THE CLRNC WAS RECEIVED. THE RTE WAS STOEN REEFI MXE AND THEN AS FILED WHICH WAS PENSY.J48.MOL.J22.VUZ..JAN..AEX.DAS6.HOU. THE PROB IS THAT REEFIE TO MXE IS ABOUT A 160 DEG R TURN. AFTER DEP; WE WERE CLRED DIRECT TO REEFI. JUST BEFORE ARRIVING AT REEFI; WE WERE GIVEN A CLRNC OF CROSS 10 NE OF EMI OR ABOVE FL260; CLB AND MAINTAIN FL280. I WAS FOCUSING ON MAKING THE CROSSING RESTRICTION; AND AGAIN FAILED TO NOTICE THE RTE IN THE FMC WAS NOT GOOD. AT REEFI; THE AUTOPLT STARTED A R TURN AND I IMMEDIATELY KNEW SOMETHING WAS NOT RIGHT. PENSY IS ONLY 7 NM N OF REEFI AND WE WERE ALMOST THERE. THE NEXT POINT ALONG THE RTE WAS EMI; SO I STARTED TO TURN BACK TO EMI. WE WERE ABOUT TO QUERY ATC ABOUT OUR RTE; WHEN HE CALLED AND ASKED WHERE WE WERE GOING. HE ASKED IF THE LAST CTLR HAD GIVEN US DIRECT TO EMI; WHICH HE HAD NOT. ATC THEN GAVE US A HDG ROUGHLY TO EMI. THERE WERE NO CONFLICTS WITH ANY OTHER ACFT. THE RESPONSIBILITY IS ULTIMATELY MINE. I HAD SEVERAL OPPORTUNITIES TO CATCH THE ERROR; WHICH I MISSED. HAD I BEEN MONITORING THE RADIO WHEN THE CLRNC WAS RECEIVED; I MIGHT HAVE CAUGHT IT THEN. I ALSO SHOULD HAVE DOUBLE CHKED THE FIRST FEW FIXES ON THE LEGS PAGE; ESPECIALLY DEPARTING AN ARPT I AM NOT FAMILIAR WITH. WE WERE BOTH VERY TIRED AND HAPPY TO BE HEADING HOME; AND I THINK WE LET OUR GUARD DOWN. IF WE HAD BEEN FLYING A -700; I DON'T THINK THIS WOULD HAVE HAPPENED. WE WOULD HAVE SEEN THE RTE WAS NOT RIGHT LONG BEFORE ARRIVING AT REEFI. ADDITIONALLY; STOEN IS ON THE PHL7 DEP; BUT REEFI IS NOT DEPICTED. IF STOEN; REEFI; EMI IS THE NORMAL RTE; THEN HAVING IT DEPICTED ON A SID WOULD HELP TO RAISE SITUATIONAL AWARENESS. FINALLY; IF THIS IS NOT A NORMAL ROUTING; CHANGING THE RTE TO MATCH WOULD ALSO HELP.