B737 ACFT ON TKOF SAW ACFT ABOVE JUST AFTER LIFTOFF IN A GAR. CTLR ISSUED RWY HDG CLRNC; BUT IN SPITE OF CTLR ATTEMPTS; BOTH ACFT HAD TO TAKE EVASIVE ACTION.

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JUST AFTER ROTATION ON RWY 22R WE SAW AN ACFT (B727) EXECUTING A GAR FROM RWY 27. THE NOSE WAS LOWERED SO THAT WE WOULD PASS BELOW THE ACFT. THE CTLR QUICKLY STATED TO 'MAINTAIN RWY HDG' INSTEAD OF TURNING L TO OUR ORIGINALLY ASSIGNED HDG OF 140 DEGS. THE CTLR THEN STATED TO 'TURN R HDG 270 DEGS. ALTHOUGH THE CTLR TRIED HARD TO PROTECT AGAINST A COLLISION; HDG INFO COULD NOT HAVE HELPED IN THIS SIT (TOO LATE). A SIMPLE 'TFC' CALL WOULD HAVE GOT OUR EYES OUT OF THE COCKPIT HAD WE BEEN LOOKING INSIDE. HAD WE NOT SEEN THE ACFT GOING AROUND AND CONTINUED WITH OUR TKOF PROFILE (INCLUDING FOLLOWING THE CTLR INSTRUCTIONS) WE WOULD HAVE COME VERY CLOSE TO HITTING. SUPPLEMENTAL INFO FROM ACN 374277 REVEALED THE FOLLOWING INFO: ON ILS APCH TO RWY 27 AT BOS IN VMC AT 700 FT AGL; GPWS 'WHOOP; WHOOP; PULL UP' STARTED SOUNDING CONTINUOUSLY. ACFT WAS ON GS; GEAR AND FLAPS WERE RECHKED IN LNDG CONFIGN (30 DEGS FLAPS). APCH WAS OVER WATER AT 300 FT GPWS 3W WAS POSITIONED TO 'OFF' AND WE INITIATED A MISSED APCH TO REAFFIRM EVERYTHING WAS OK WITH THE ACFT. AS WE STARTED THE PUBLISHED MISSED APCH; TWR ISSUED A L TURN TO 140 DEGS. A B737 WAS TAKING OFF ON RWY 22R. TWR ASKED IF WE HAD THEM IN SIGHT. WE DID (SLIGHTLY BELOW US AND CLOSE IN ON THE R SIDE). TWR ADVISED US TO MAINTAIN VISUAL SEPARATION. BOTH ACFT WERE IN L TURNS TO 140 DEGS. WITH OUR BELLY UP TO THE OTHER ACFT; IT WAS IMPOSSIBLE TO MAINTAIN VISUAL CONTACT. ON TCASII; OTHER ACFT WAS OBSERVED DIRECTLY BELOW US AT -100 FT AND CLBING. NO RA WAS ISSUED BECAUSE GPWS HAD BEEN DISABLED. IN ORDER TO MAINTAIN VISUAL SEPARATION; WE MADE AN IMMEDIATE REVERSAL TO A R TURN. OTHER ACFT WAS OBSERVED PASSING DIRECTLY BELOW US IN A L TURN. RWY 27 AND RWY 22L ACFT ARE ON DIFFERENT FREQS; AND THEREFORE; UNAWARE OF INSTRUCTIONS GIVEN TO OTHER ACFT; AND UNABLE TO TALK TO EACH OTHER.