NMAC OPERROR BTWN AN ACR JET AND AN UNKNOWN ACFT.

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ON SADDE ARR WE WERE CLRED FROM 7000 FT OVER SMO TO 2500 FT ON A HDG OF 070 DEGS. DSNDING THROUGH 6000 FT WE WERE RECLRED TO MAINTAIN 4000 FT. AFTER THAT WE WERE CLRED AGAIN TO 2500 FT AND GIVEN A 160 DEG HDG. ATC ASKED IF WE HAD THE ARPT AND I (CAPT PNF) SAID NO; THAT WE COULD JUST BARELY SEE THE RACETRACK. (WE WERE VECTORING FOR RWY 24R LAX). HE THEN GAVE US A 230 DEG HDG BUT DID NOT CLR US FOR AN APCH. AS WE APCHED THE LOC THE FREQ WAS VERY BUSY AND WE WERE NOT ABLE TO CONTACT APCH AND TELL THEM THAT WE WERE GOING THROUGH THE LOC. AT 2600 FT WE GOT A TCASII 'MONITOR VERT SPD' WHICH WAS FOLLOWED IMMEDIATELY BY AN RA; 'CLB; CLB.' THE FO DISENGAGED THE AUTOPLT AND BEGAN AN IMMEDIATE CLBING R TURN. AT 2800 FT WE WERE ABLE TO CONTACT APCH AGAIN AND INFORMED HIM OF OUR TCASII ACTION. HE CLRED US TO MAINTAIN 3000 FT AND TURN R TO A HDG OF 270 DEGS. RIGHT AFTER THAT HE GAVE US A HDG OF 340 DEGS AND LATER TURNED US R DOWNWIND FOR ANOTHER APCH. THE FO AND I BOTH AGREE THAT WE WERE NEVER CLRED FOR EITHER A VISUAL OR INSTR APCH. THE CONDITIONS WERE THE USUAL LATE AFTERNOON SUN AND HAZE WITH RESTR VISIBILITY. THEY WERE RPTING VISUAL CONDITIONS BUT LOOKING INTO THE SUN AND HAZE WE WERE NOT ABLE TO GET VISUAL AND WE TOLD THEM SO. WE WERE NOT ADVISED OF PARALLEL TFC ON THE L SIDE OF THE COMPLEX. THIS WAS PROBABLY BECAUSE OF THE HIGH WORKLOAD THE CTLR WAS UNDER. I TALKED TO HIS WATCH SUPVR THE NEXT MORNING AND HE SAID THAT WE WERE THE LAST ACFT TO BE INCLUDED IN THE VISUAL (ALTHOUGH WE WERE NOT VISUAL) AND THAT EVEN AS WERE EXPERIENCING THE EVENT HE WAS IN THE NEXT ROOM ACQUIRING 2 MORE PEOPLE TO GO OVER TO THE ILS CONFIGN. HE THOUGHT THE PROB WAS THAT WE GOT CAUGHT 'ON THE CUSP' BTWN VMC AND IMC OPS. IN THE FUTURE GIVEN A PARALLEL OP I WILL TAKE IT UPON MYSELF TO INTERCEPT WITHOUT AN INTERCEPT CLRNC RATHER THAN FLY THROUGH AND ENCOUNTER TFC ON THE OTHER SIDE.