B737-300 ACFT WAS CLRED ONTO RWY AS OTHER ACFT WERE ON APCH. TWR CLRED ACFT ON APCH TO LAND RWY 33; BUT FLC SAID 'UNABLE;' SO TWR CLRED THEM TO LAND RWY 36. RPTR ACFT WAS ON RWY 36 AND APPARENTLY THE LCL CTLR FORGOT. ACFT ON APCH DID A GAR AND TWR HAD RPTR ACFT CLR THE RWY.

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CLR NIGHT; NW WINDS; HVY VOLUME ON DEPS AND ARRS. WE WERE #3 IN LINE FOR TKOF BEHIND AN ACR X AND AN ACR Y FLT. WHEN WE SWITCHED TO TWR; WE HEARD CTLR CLR ANOTHER ACR X FLT ON APCH; 'ACR X XXX CLRED TO LAND RWY 33.' REPLIED; 'ACR X XXX UNABLE RWY 33.' TWR THEN SAID; 'ROGER ACR X XXX; YOU'RE #2 FOR RWY 36; START SPD REDUCTION.' 'ACR X XXX; ROGER.' TWR NOW CLRED THE OTHER ACR X ACFT WHO WAS #1 FOR TKOF RWY 36. THE #2 ACFT IN LINE; AN ACR Y FLT; WAS ALSO CLRED FOR TKOF. I BELIEVE TWR NOW CLRED WHOEVER WAS #1 ON APCH TO LAND ON RWY 33; BUT UNSURE OF EVENTS BECAUSE WE WERE #1 FOR TKOF; AND WERE FINALIZING CHKLIST ITEMS. WE RECEIVED CLRNC TO TAXI INTO POS AND HOLD; AND AS I TAXIED ONTO RWY WE NOTICED LIGHTS ON FINAL; BUT WERE UNABLE TO ACCURATELY DETERMINE DISTANCE OR ALT. WE TURNED ON RWY TURNOFF AND TAXI LIGHTS TO ILLUMINATE OUR POS ON RWY AND LISTENED TO TWR GIVE PREVIOUS DEPS INSTRUCTIONS TO TURN UP THE RIVER AND CONTACT DEPS. CTLR WAS BUSY TALKING AND AS WE WONDERED WHY WE WERE NOT GETTING OUR OWN TKOF CLRNC WE HEARD 'TWR; THERE IS AN ACFT ON THE RWY; ACR X XXX IS GOING AROUND.' A NEW TWR CTLR (SUPVR?) CAME ON RADIO AND ASKED US (ACR Y) TO TAXI UP AND TURN L OFF THE RWY. THERE WAS ANOTHER ACFT ON FINAL CLOSE BEHIND ACR X XXX. WE ARE NOT SURE HOW LOW ACR X CAME BEFORE GOING AROUND ON TOP OF US; BUT HE MADE OUR PLANE RATTLE. I NEVER HEARD TWR GIVE HIM CLRNC TO LAND; AND I BELIEVE CTLR FORGOT HE WAS ON FINAL TO RWY 36 INSTEAD OF RWY 33. CTLR WAS OVERLOADED. SHOULD NOT EXPECT CARRIER JETS TO LAND ON RWY 33 AT DCA.