ATX H25B ON IFR FLT TO EWR INVOLVED IN ACR NMAC WHEN APPARENTLY THEIR FLT PLAN PROCESSED FOR TEB.

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AN INST FLT PLAN WAS FILED FROM HPN TO EWR. APCH CHARTS FOR NEWARK RWY 22L WERE CREW BRIEFED. WE DSNDED TO 2000 FT AND WERE ASSIGNED HDG FOR LOC INTERCEPT. NEW YORK APCH XMITTED A CLRNC FOR RWY 19; WHICH DOES NOT EXIST AT NEWARK; BUT DOES AT TEB. AFTER INTERCEPTING THE EWR RWY 22L LOC; FO SWITCHED TO NEWARK TWR AND RPTED INBOUND ON ILS. NEWARK TWR WAS SURPRISED BY THE CALL AND ASKED IF WE TOOK OFF FROM TEB. AFTER NEWARK TWR REALIZED THAT WE WERE LNDG AT NEWARK; WE WERE THEN INSTRUCTED TO MAKE A R TURN TO A HDG OF 280 DEGS. THIS IS THE MISSED APCH HDG FOR EXECUTION OF A MISSED APCH AT TEB. BEFORE MAKING THE ASSIGNED TURN; I SAW AN AIRLINER ABOVE OUR ACFT APPROX 200-500 FT ABOVE OUR ALT. I THEN TURNED SLIGHTLY TO THE L; REDUCED SPD TO FALL INTRAIL OF THAT ACFT; DSNDED TO 1800 FT; AND THEN TURNED TO MY ASSIGNED HDG OF 280 DEGS. AFTER SEVERAL VECTORS; WE RETURNED TO NEWARK FOR A LNDG ON RWY 29. AFTER LNDG; GND CTL ASKED IF I WOULD CALL THE TWR. WE DISCUSSED THE SIT AND HE INDICATED THAT HE WAS INTERESTED IN DETERMINING WHY IT ALL OCCURRED IN THE FIRST PLACE; AND WAS INTERESTED IN LEARNING HOW THESE TYPES OF CONDITIONS COULD BE AVOIDED IN THE FUTURE. APPARENTLY DURING THE ATC FUNCTION OF HANDLING OUR FLT; A MISTAKE WAS MADE BY ATC. THE WRONG INFO WAS COMMUNICATED BTWN CTLRS AND WE WERE ASSUMED TO BE WHERE WE WEREN'T (MAKING AN ILS APCH TO RWY 19 AT TEB). THE FLC PREVENTED A MIDAIR COLLISION BY BEING ABLE TO RECOGNIZE THE MISCUE CAUSED BY ATC. WE RECOGNIZED THAT 2 ACFT WERE MAKING THE SAME ILS APCH TO THE SAME RWY AND TOOK THE NECESSARY CORRECTIVE ACTION. VMC CONDITIONS CONTRIBUTED TO THE SUCCESSFUL RECOGNITION AND EVASIVE ACTIONS THAT PREVENTED A POSSIBLE MIDAIR COLLISION. SUPPLEMENTAL INFO FROM ACN #565191: MULTIPLE LEGS. WITHIN 135 DUTY REGS. NAVIGATION SYS FOR ACFT IS LOW FUNCTIONING AND LIMITED. INTERMITTENTLY WOULD NOT ACCEPT FIXES ON AIRWAYS AND APCHS. CAPT DID NOT WEAR A HEADSET AND LISTENED THROUGH SPEAKER SYS. FO DID WEAR HEADSET. FIRST TIME THIS CREW HAD FLOWN TOGETHER AND CRM WAS DIFFERENT WITH CAPT. UPON SEARCHING FOR THE APCH PLATES FOR RWY 19 AT EWR; I DISCOVERED THAT NONE EXISTED. I ALERTED THE CAPT. CAPT INSTRUCTED ME TO CALL THE EWR TWR. TWR QUERIED AS TO WHAT ARPT WE INTENDED TO LAND. I REPLIED; 'NEWARK.' EWR TWR GAVE US A TURN TO THE R AND SENT US TO DEP.