ACR MLG CREW LANDS ON CLOSED RWY. ARPT CONSTRUCTION ACTIVITY.

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RADAR VECTORED FOR AN ILS APCH TO RWY 22L AT EWR. AFTER BEING CLRED FOR THE APCH; WE SWITCHED TO EWR TWR OVER TETERBORO. WE CHKED IN WITH TWR AND WERE CLRED TO LAND ON RWY 22L. AT THE REQUEST OF THE CAPT; IN ORDER TO EXPEDITE OPS; I ASKED EWR TWR IF RWY 22R WAS AVAILABLE FOR LNDG. AS NO RESPONSE WAS OBTAINED FROM THE TWR TO OUR FIRST XMISSION; WE ASKED AGAIN IF RWY 22R 'WAS AVAILABLE.' AFTER OUR SECOND XMISSION EWR TWR REPLIED; 'AFFIRMATIVE; CLRED TO LAND 22R.' THIS IS THE XMISSION BOTH THE CAPT AND MYSELF REMEMBER HEARING FROM THE TWR CTLR. I THEN (COPLT) REPLIED TO THE XMISSION BY SAYING; 'ROGER; CLRED TO LAND RWY 22R.' UPON TOUCHDOWN ON RWY 22R WITH ENGS IN REVERSE AND BRAKES APPLIED (DECELERATING THROUGH 80 KTS) THE TWR CTLR FRANTICALLY XMITTED FOR US TO GAR. WHILE THE TWR WAS XMITTING DURING OUR ROLLOUT PHASE WE FINALLY WERE ABLE TO SHIFT OUR ATTN TO THE 'CONSTRUCTION' AT THE FAR END OF RWY 22R. RWY VISIBILITY WAS VERY RESTR DUE TO HAZE AND FLYING INTO THE SETTING SUN. TWR WAS NOT AWARE OF OUR 'ENERGY' (FLT PHASE) AVAILABLE WITHIN THE COCKPIT WHEN THEY REQUESTED US TO GAR. THE REQUESTED MANEUVER WAS IMPOSSIBLE TO EXECUTE WITHIN THE 'ENERGY AVAILABLE' AND RWY LENGTH REMAINING. WE BROUGHT THE ACFT TO A STOP AND EXITED THE RWY AT THE 'HIGH SPD' TXWY WELL BEFORE THE POINT WHERE THE CONSTRUCTION WAS BEING ACCOMPLISHED. AT NO TIME DURING ANY PHASE DID I FEEL WE WERE NOT IN FULL CTL OF THE SIT. WE CLRED THE RWY WITHOUT INCIDENT; AND PROCEEDED TO OUR GATE. UPON ARR; THE CAPT TALKED TO THE TWR SUPVR.' THE CAPT REQUESTED A 'REVIEW' OF THE TAPES FOR ANALYSIS BY OURSELVES AND OUR SAFETY REPRESENTATIVES. I SINCERELY FEEL THAT THE 'NONSTANDARD' TERMINOLOGY USED BY THE TWR CTLR IN CONJUNCTION WITH THE 'LACK' OF EMPHASIS ON THE ATIS FOR THE CLOSURE OF RWY 22R LED DIRECTLY TO THIS INCIDENT. ADDITIONALLY; WHEN I READ BACK THE LNDG CLRNC FOR RWY 22R THIS WAS 'THE LAST OPPORTUNITY' FOR THE TWR CTLR TO HAVE CAUGHT THE ERROR. I TRULY BELIEVE THAT CONFUSION AND BAD COM WERE THE CONTRIBUTING FACTORS!