FLC OF A DC10-40 OVERSHOT FINAL DURING A VISUAL APCH DUE TO A STRONG XWIND ON BASE LEG. TWR CTLR ALERTED THEM TO THEIR ERROR.

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SOCAL APCH ASSIGNED A 070 DEG HDG AFTER SMO VORTAC; DSCNT FROM 7000 FT TO 4000 FT WHILE ON RADAR DOWNWIND FOR RWY 24R AT LAX. FO WAS FLYING; I WAS CAPT AND ALL 3 PLTS WERE TIRED DUE TO FLYING ALL NIGHT. WX WAS GOOD; HOWEVER; STRONG SANTA ANA CONDITIONS WERE DRIFTING US TOWARDS THE LNDG RWY. JUST PRIOR TO ABEAM POS TO ROMEN; APCH CLRED US FOR A VISUAL APCH; INSTRUCTED US TO TURN BASE WITHIN 1 MI; INFORMED US THAT WE HAD TFC AT OUR 1 O'CLOCK POS FOR THE S COMPLEX; AND DIRECTED US TO CONTACT TWR. AT THE TIME WE WERE DSNDING THROUGH 5500 FT MSL AND I FELT WE WERE TOO HIGH TO SAFELY COMPLETE THE APCH. I TOLD THE FO I THOUGHT HE WAS 'TOO HIGH'; BUT FAILED TO INSIST THAT HE EXTEND THE DOWNWIND. ALL 3 OF US WERE SO PREOCCUPIED WITH MONITORING THE STEEP DSCNT AND LOOKING FOR OUR TFC (WHICH WE NEVER SPOTTED) THAT WE DID NOT REALIZE THAT WE HAD COMPLETELY OVERSHOT THE N COMPLEX AND WERE PERFECTLY ALIGNED TO LAND ON RWY 25R. THIS OCCURRED EVEN THOUGH WE HAD TUNED; IDENTED AND SELECTED THE ILS FOR RWY 24R. WE DIDN'T REALIZE THE MISTAKE UNTIL LAX TWR QUERIED US IF WE WERE GOING TO 'CORRECT N.' WE STILL HAD ENOUGH DISTANCE TO CORRECT BACK TOWARDS RWY 24R AND THE TWR ULTIMATELY CLRED US TO LAND ON RWY 24L. FATIGUE; LACK OF SITUATIONAL AWARENESS (HIGH ALT; STRONG DRIFT); DISTR (LOOKING FOR TFC) AND POOR LEADERSHIP (I SHOULD HAVE INSISTED THAT WE EXTEND THE DOWNWIND) CONTRIBUTED TO THIS ERROR. GOOD WX AND LACK OF PROXIMATE TFC PREVENTED THIS ERROR FROM BECOMING A DISASTER.