B767 AT NIGHT CREW HAD SMOKE FROM THE EXTERIOR OF THE APU AFTER STARTING AT IAD.

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STARTED APU JUST PRIOR TO PARKING AT GATE. PARKED ACFT. SHUT DOWN #2 AND #1 ENG. MECH INFORMED SMOKE COMING FROM APU. REQUIRED GND PWR HOOKUP SO APU COULD BE SHUT DOWN. APU EGT NOTED APPROX 350. EICAS DISPLAYED LOW OIL QUANTITY. DISCUSSED SHUTTING DOWN APU MANUALLY BEFORE GND PWR CONNECT. APU AUTO SHUTDOWN. SEVERAL ATTEMPTS TO REESTABLISH GND COM AND GND PWR MADE PA AND INFORMED PAX. FIRE EQUIP ARRIVED; ALERTED BY IAD GND. ESTABLISH COM WITH FIRE CREW THROUGH FIREMAN HAND RADIO IN COCKPIT. INFORMED LOW OIL NO FIRE INDICATION. REQUEST TO PULL APU FIRE HANDLE/BOTTLE DECLINED BY FIRE CREW. IE; MEN IN APU COMPARTMENT CAPT REQUEST WE USE OUR ACFT FIRE PROTECTION SYS IF EXTINGUISHER REQUIRED. CAPT MADE 2 REQUESTS TO USE OUR SUPPRESSION SYS IF NEEDED NOT FIRE CREW HOSE. FIRE DEPT DID FIRE AGENT INTO APU. WROTE UP EICAS LOW OIL QUANTITY AND AUTO SHUTDOWN AFTER SECURING ACFT. RECOMMENDATION: WHEN APU QUIT; PARKING CHK WAS COMPLETE. EMER LIGHTS WERE IN 'OFF' POS. SUGGEST EMER LIGHTS REMAIN ARMED UNTIL ALL PAX ARE OFF ACFT OR ACFT GOING TO BED. THIS WILL PREVENT A DARK CABIN IN BOTH APU AND EXTERIOR PWR FAILURE AT GATE. ALSO; THOUGHT TO VERIFY VALIDITY OF APU FIRE LIGHT BUT DECIDED EXTERIOR HORN AND LIGHT MAY FALSELY ALARM THE FIRE CREW.