MD SUPER 80 FLC INADVERTENTLY LANDED ON THE WRONG PARALLEL RWY AT EWR DUE TO UNEXPECTED CHANGE IN INST APCH PROC; RECONFIGURING THE ACFT AND LATE LNDG CLRNC.

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ATIS RPTED LNDG AT EWR VIA ILS APCH TO RWY 22L. NEW YORK APCH ASSIGNED VOR/DME RWY 22L APCH. THE CAPT MISTAKENLY ASSUMED ASSIGNED APCH WAS TO VOR RWY 22R. DUE TO THE HIGH WORKLOAD OF INTERCEPTING THE INBOUND COURSE; DSNDING TO STEPDOWN ALTS; CONFIGURING THE ACFT; AND REDUCED VISIBILITY; THE RADIO CHANGE-OVER TO TWR FREQ OCCURRED LATE. THIS CAUSED THE RWY SELECTION ERROR TO GO UNDETECTED BY BOTH THE CAPT AND FO UNTIL ROLLOUT. THIS RESULTED IN OUR LNDG ON RWY 22R AFTER BEING CLRED TO LAND ON RWY 22L. SUPPLEMENTAL INFO FROM ACN 556943: ORD BASED CHK AIRMAN (CHK CAPT) IOE WITH STUDENT FO ON FIRST LEG OF FIRST IOE SEQUENCE. LNDG AT EWR ARPT. EWR ATIS RPTED ILS RWY 22L APCHS WERE BEING CONDUCTED AT EWR ARPT. I BRIEFED THE ILS RWY 22L APCH. NY APCH ACTUALLY ASSIGNED US THE VOR DME RWY 22L APCH. I MISHEARD THE CLRNC TO READ 'CLRED VOR RWY 22R.' NY APCH GAVE US A SHORT VECTOR TO INTERCEPT THE INBOUND COURSE 2 MI INSIDE THE TETERBORO VOR; 8 MI FROM THE RWY. DUE TO THE HIGH WORKLOAD; INTERCEPTING THE INBOUND COURSE 8 MI FROM THE RWY WITH MARGINAL VISIBILITY; DSNDING DOWN TO A STEP DOWN ALT; CONFIGURING THE ACFT FOR LNDG AND SWITCHING TO TWR CLOSE IN; THE RWY ASSIGNMENT MISUNDERSTANDING WAS NOT DETECTED BY EITHER ME OR THE FO AND WE LANDED ON RWY 22R INSTEAD OF THE ASSIGNED RWY 22L. WE HEARD NO CALLS FROM EWR TWR ADVISING US THAT WE WERE NOT LNDG ON THE ASSIGNED RWY.