ACR X FLC ON OAK ILS-11; EXECUTES GAR DUE TO GS DEFLECTION. DURING GAR; ACR X ISSUED TFC ALERT BY OAK LC ON UNKNOWN TFC.

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WE WERE CLRED FOR THE ILS II AT OAK; MAINTAIN 160 KTS UNTIL PLAZA; CROSS PLAZA AT OR BELOW 1800 FT. THE APCH WAS AUTO COUPLED. WE DESCENDED OUT OF 3000 FT WITH GLIDESLOPE CAPTURE. WE WERE FOLLOWING AN ACFT ON SHORT FINAL FOR RWY 11. AFTER THAT TFC LANDED; THE TWR CTLR CLRED A B767 INTO POS AND HOLD FOR RWY 11. WHILE DESCENDING ON GLIDESLOPE IN IMC; THE GLIDESLOPE SIGNAL STARTED +/- 2 DOT DEFLECTIONS DUE TO INTERFERENCE OF THE ACFT ON THE RWY. WE INITIATED AND ANNOUNCED OUR 'GAR' AT APPROX 2200 FT. THE TWR CTLR ANNOUNCED; 'ACFT X; TURN TO 090 AND CLB TO 1600 FT; NOW!' ALTHOUGH WE HAD INITIATED AN AUTO COUPLED CLB OUT AT 2200 FT; I IMMEDIATELY DISCONNECTED THE AUTO PLT AND BEGAN TO HAND FLY THE 090 HEADING DUE TO THE URGENT TONE OF THE CTLRS VOICE. I BEGAN TO SORT OUT OUR SITUATION (IE CLB? TO AN ALTITUDE BELOW ME?); WHEN THE TWR CTLR FORCEFULLY SHOUTED OUT; 'TFC ALERT! TFC ALERT! ACFT X TURN L IMMEDIATELY TO 360 DEG; CLB MAINTAIN 2500 FT! THE TWR CTLR BEGAN CONTINUALLY ANNOUNCING A CLOSING ALTITUDE AND DISTANCE. IT WAS UNCLEAR IF OUR TFC WAS ABOVE OR BELOW US. I JUDGED OUR BEST CHANCE OF ESCAPE WAS THE 360 DEG HEADING; I INITIATED A STEEP BANK TO AVERT A COLLISION WHILE IN IMC CONDITIONS. THE CLOSEST TFC ALERT I RECALL WAS 400 FT AND 1/2 MILE. WHEN COLLISION WAS NO LONGER A FACTOR WE WERE HANDED OFF TO SIERRA APCH. SIERRA APCH ASKED US THE NATURE OF OUR EMER (WE NEVER HAD TIME TO DECLARE ONE.) AND INTENTIONS; AT OUR REQUEST; WE WERE VECTORED FOR ANOTHER APCH TO ILS 11 AT OAK. ON OUR HAND OFF TO OAK TWR; THE CTLR APOLOGIZED FOR THE MISCOMMUNICATION AND MISDIRECTION OF OUR ACFT. THE FACTORS THAT CONTRIBUTED TO THIS NEAR MID AIR COLLISION WERE: INCLEMENT WX AT NIGHT; ACFT INTERFERENCE WITH THE GLIDE SLOPE SIGNAL. THIS WAS DUE TO THE TIGHT TKOF AND DEP SEQUENCE AT OAK. ACFT SHOOTING THE VOR 9 APCH SIMULTANEOUSLY WITH THE ILS 11 APCH AT OAK. I WOULD LIKE TO COMMEND THE QUICK SUPPORTIVE ACTIONS BY MY FO. WITHOUT IT; THE RESULTS WOULD HAVE BEEN TRAGICALLY DIFFERENT.