FLT CREW OF B737 ARRIVING JAN AFTER DARK ON VISUAL APCH; NEARLY LANDED AT MBO.

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THIRD AND FINAL LEG OF DAY. LEG #2 DELAYED 2 HRS DUE TO TSTM WHICH PUT EVERYTHING BEHIND; SO WE ARRIVED AFTER TWR CLOSED. ASOS GAVE JAN WX 500 FT BROKEN; 6 BR; BUT A DEPARTING FLT RPTED SCATTERED CLOUDS AND SAID A VISUAL APCH SHOULD BE NO PROB. WE TOLD ZME TO SET US UP FOR THE ILS ANYWAY. CLRNC WAS DIRECT JAN VOR AND CLRED ILS RWY 16L -- NOT EXACTLY LEGAL BECAUSE THE VOR IS NOT PART OF THE APCH; BUT WE FIGURED WITH MOSTLY VMC WE COULD MAKE IT WORK. WE SIGHTED THE ARPT ONCE DURING DSCNT; BUT ONLY BRIEFLY DUE TO A CLOUD LAYER AT LOWER ALT. ABOUT 5 MI E OF JAN VOR; CAPT (PF) RPTED RWY IN SIGHT. I SAW IT TOO; INFORMED ZME; WHO CLRED US FOR A VISUAL APCH. AFTER CONFIGURING AND FINISHING CHKLISTS; I NOTED THAT ALLEN (JA NDB) WAS STRAIGHT AHEAD; BUT JAN VOR WAS TO THE R; AND TOLD THE CAPT 'I DON'T THINK THAT'S IT.' SIMULTANEOUSLY HE NOTED THAT THE ILS WAS NOT GIVING PROPER INDICATIONS. WE WENT AROUND; THEN SIGHTED THE CORRECT RWY STRAIGHT AHEAD ABOUT 6 MI. REST OF ARR WAS UNEVENTFUL. ALT AT GAR WAS APPROX 1100-1200 FT AGL. CONTRIBUTING FACTORS: DELAYS; LATE NIGHT; NO FOOD; FATIGUE (DAY #5 FOR BOTH PLTS); CONFLICTING WX RPTS; AND NOT STAYING WITH INST ARR. ALSO; THE CAMPBELL ARPT (MBO) IS ON THE APCH CHART AND HAS SIMILAR RWY ORIENTATION (RWY 17/35); BUT OUR COMPANY HAS NOT MENTIONED THE POTENTIAL CONFUSION BY BULLETIN. WE WILL RECOMMEND THAT. THE 4400 FT RWY WOULD HAVE MADE AN INTERESTING STOP; AS WELL AS PROBABLY COSTING US CERTIFICATE ACTION OR WORSE. BACKING UP THE VISUAL APCH WITH INSTS SAVED OUR HIDES -- SOMETHING I'VE ALWAYS BELIEVED AND HAS NOW BEEN CONFIRMED THROUGH AN INTENSE LESSON!