ACR X MADE APCH TO WRONG RWY HAD LTSS WITH ACR Y. ACR Y WAS RADAR VECTORED OFF APCH AND HAD CONFLICT WITH VFR ACFT. SYS ERROR.

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ACR X SETTING UP AND BRIEFING ILS RWY 25L (CAT I) WE WERE DELAY VECTORED AND THEN VECTORED OVER THE TOP OF ARPT AT 7000 FT MSL FOR APCH RWY 24R. IN SPITE OF COMPLETING ALL CHKLISTS AND IDENTING OF NAVAIDS; WE FAILED TO CHANGE BOTH ILS FREQS FROM RWY 25L OVER TO RWY 24R AND WE INTERCEPTED THE COURSE INBOUND TO THE WRONG RWY APPROX 15 MI OUT 2500 FT MSL; AND APPROX 2 MI IN BACK OF ANOTHER ACFT. THE CTLR CAUGHT OUR MISTAKE AND VECTORED US BACK TO THE N RWY. CREW FATIGUE A FACTOR; END OF 12 HR DAY. APCH CTL LEVEL OF ACTIVITY A FACTOR; A LOT OF TALK ON THE RADIO. SUPPLEMENTAL INFO FROM ACN 298747: DURING ILS APCH TO RWY 25L AT LAX; AT ABOUT 10 DME; FULL LNDG CONFIGURED; ATC SUDDENLY AND EXCITEDLY TOLD US TO ACCELERATE AND CLB IMMEDIATELY. WE COMPLIED AS FAST AS POSSIBLE AND ASKED WHAT THE PROB WAS. ATC (APCH) SAID AN ACR X HAD OVERSHOT RWY 24R WHEN TURNING TO INTERCEPT FROM THE N AND WAS JUST ABOUT TO RUN INTO US FROM THE REAR. THERE WAS AT LEAST 30 KTS OF WIND FROM THE N WHICH CONTRIBUTED TO THIS. WE NEVER SAW THIS AIRLINER (WX) OR HAD ANY TCASII WARNING. WE HAD BEEN CLBED STRAIGHT AHEAD TO ABOUT 3500 FT THEN TURNED TO ABOUT 170 DEG HDG AFTER CLB. WE WERE THEN AT 3500 FT AND TURNED TO A DOWNWIND HDG OF 070 DEGS AND WHILE IN THIS TURN WE GOT A TCASII WARNING FOR ANOTHER ACFT CLOSE (LESS THAN 1 MI) ON OUR R. ATC SPOKE UP AGAIN. THEY SAW THE TFC (ACFT Z) ABOUT WHEN OUR TCASII WENT OFF. ATC THEN IMMEDIATELY TOLD US TO TURN TO 070 DEGS; WHEN WE WERE ALREADY TURNING. THIS WAS APPARENTLY VFR TFC IN THE VFR CORRIDOR AREA ABOVE LAX.