B727 FLC ISSUED GAR AT BOS ARPT. WHILE ON VECTOR; FLC RECEIVED 2 TCASII ALERTS FROM 2 OTHER ACFT ON VECTORS FOR APCH. TRACON SUPVR ADVISED CTLR ADDED TO CONFUSION BY ISSUING INCORRECT HDGS.

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ILS RWY 33L BOS. SEPARATION ON APCH WAS MINIMAL REFING ACFT IN FRONT OF US. AT ATC REQUEST (APCH CTL) WE WERE MAINTAINING 170 KIAS TO THE MARKER. ON CONTACT WITH TWR WE WERE ADVISED TO EXPECT LNDG CLRNC ON SHORT FINAL; AND THEN WERE IMMEDIATELY TOLD TO GAR; MAINTAIN 3000 FT; HDG 330 DEGS. AFTER BEING GIVEN A SUBSEQUENT R TURN; WE WERE TURNED FURTHER R TO; I BELIEVE; 210 DEGS. AT THIS POINT TCASII ADVISED 'TFC.' THROUGH A BREAK IN CLOUDS; I OBSERVED ACFT Y CORRESPONDING TO THE TCASII LOCATION (FO WAS FLYING). ATC (NOW APCH CTL AGAIN) GAVE US A TURN TO 120 DEGS. IMMEDIATELY THEREAFTER; THE TCASII COMMANDED 'MONITOR VERT SPD;' INDICATING A HIGH RATE OF CLB REQUIRED. CLB WAS IMMEDIATELY INITIATED AND THEN ATC ADVISED US TO 'CLB TO 4000 FT -- CLB NOW!' I ADVISED APCH WE WERE ALREADY CLBING. AT 4000 FT; TCASII ADVISED CLR OF CONFLICT. MOST OF THIS WAS IN CLOUDS. I DID NOT SEE THE OTHER ACFT. IN A SUBSEQUENT PHONE CALL TO APCH CTL; THE SUPVR ADVISED HE 'THOUGHT I MIGHT HEAR FROM YOU;' INDICATED THE CTLR 'GAVE [US] THE WRONG HDG.' WHEN THE SUPVR LOOKED UP; WE HAD ACHIEVED LEGAL SEPARATION. THIS WAS A SECOND ACFT; ACR Z; A DC10. FIRST ACFT TA WAS NOT A FACTOR.