AN ACR B727 FLC TURN OFF THEIR STAR COURSE AND DSND BELOW THEIR ASSIGNED XING POINT ALT AND OVERSHOT THEIR TURN TO FINAL APCH. ALL OF THESE EVENTS WERE IN PART DUE TO ARTCC AND APCH CTL ERRORS AND FREQ AND TFC CONGESTION ACCORDING TO THE RPTRS.

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UPON ARR INTO THE LAX AREA WE WERE ON THE SADDE 6 STAR HDG TOWARD FILLMORE WHEN THE CTLR GAVE US HDG VECTORS. THEN WE WERE CLRED TO FILLMORE. OUR NEXT INSTRUCTION WAS TO CROSS THE SANTA MONICA VOR AT 7000 FT. WE TURNED TO GO TO SANTA MONICA VOR (ALTHOUGH A DEBATE WAS HELD AS TO WHETHER OR NOT THE CTLR WANTED US TO RESUME THE REMAINDER OF THE ARR PROC). NEXT CAME AN INSTRUCTION FROM ATC TO MAKE AN IMMEDIATE TURN. OUR NEXT INSTRUCTIONS WERE TO CROSS SANTA MONICA VOR AT 7000 FT; THEN DSND RAPIDLY TO 2500 FT. IN THE RECENT LIGHT OF CONFUSION OUR ATTNS WERE NOT FULLY FOCUSED ON THE TASK IN HAND. CONSEQUENTLY; THE ACFT CROSSED THE VOR AT 6600 FT DSNDING TO 2500 FT. AT NO TIME HAD ANYONE TOLD US WHICH RWY TO EXPECT AND SINCE WE WERE PARKING ON THE S SIDE OF THE FIELD WE WERE PREPARED FOR LNDG ON RWY 25L/R. WHEN THE FINAL CTLR GAVE US OUR INTERCEPT TURN FOR RWY 24R; I FRANTICALLY SEARCHED FOR THE APPROPRIATE APCH PLATE AND DIALED IN THE LOC FREQ. AS WE LEVELED OUR WINGS ON THE ASSIGNED INTERCEPT HDG; THE NEW LOC SIGNAL CAME IN. WE HAD TO RECAPTURE THE NEEDLE. AS WE STARTED OUR TURN; ATC TOLD US TO TURN FOR THE RE- INTERCEPT. THE ATC CTLRS WERE EXTREMELY BUSY; WITH NO TIME TO INTERJECT OUR QUESTIONS OF WHETHER WE WERE SUPPOSED TO RESUME THE ARR PROC. WE WERE ALSO LEFT IN THE DARK ON WHICH RWY WE WERE BEING VECTORED FOR; ALTHOUGH I BELIEVED IT WAS ALSO A 'TIGHT TURN ON.'