DUE TO WX AND ATC COM; AN SF340 CREW REPORTS NOT CLEARLY HEARING AN ATIS MSG ADVISING RWY CLOSURE AND SO LANDED ON A CLOSED PORTION OF A RWY.

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THE EVENT WAS A RESULT OF MISSED INFO. I; AS CAPT MISSED THE NOTAM AND DID NOT HEAR THE INFO ON ATIS. WE HAD SEVERAL DISTRS DURING THE APCH AND LNDG. LANDED AT ZZZ ON RWY 13 ON LAST 1/3 OF CLOSED PORTION OF RWY. DID NOT REALIZE PORTION OF RWY WAS CLOSED. WHEN RECEIVING ATIS INFO WE DID NOT COPY INFO THAT RWY WAS CLOSED. WE WERE AT THAT TIME DEVIATING THROUGH WX; AND PERTINENT INFO MAY HAVE BEEN LOST TO STATIC OR DUE TO DISTR. I MONITORED ATIS THROUGH 2 CYCLES AND DO NOT RECALL HEARING THAT PORTION OF RWY WAS CLOSED. IN ADDITION DURING APCH; WE HAD SEVERAL COMS WITH APCH ABOUT OUR CALL SIGN; WHICH MAY HAVE DISTR US. ON SHORT FINAL; I NOTICED RWY MARKINGS AND ADJUSTED FLT PATH SLIGHTLY TO AVOID CLOSED AREA; BUT TOUCHED DOWN IN LAST 1/3 OF CLOSED AREA. I FELT THE ADJUSTMENT OF FLT PATH WAS SAFER THAN ATTEMPTING A GAR CONSIDERING THE ALT AND THE FACT THAT THE LNDG AREA APPEARED CLR. WE REALIZED AT TOUCHDOWN THAT WE HAD NOT CLRED THE CLOSED PORTION. ONCE THE EVENT WAS IDENTED; WE TALKED TO ATC AND CONFIRMED TOUCHDOWN IN CLOSED AREA. WE REVIEWED THE NOTAMS WE HAD MISSED AND REVIEWED ATIS; WHICH HAD SINCE CHANGED. I THINK THE EVENT COULD HAVE BEEN AVOIDED BY ADDING ANOTHER LAYER OF PROTECTION VIA ATC. PERHAPS A REMINDER FROM APCH AS THE CLRNC IS ISSUED THAT THE LNDG RWY HAS BEEN MODIFIED; OR FROM TWR AS CLRNC TO LAND IS ISSUED; IE; 'CLRED TO LAND RWY 13; FIRST XXX FT CLOSED.'