A B757-200 FLT CREW NOTICED LOW OIL PRESSURE AND QUANTITY IN THE #2 ENG. THEY DECLARED AN EMERGENCY AND DIVERTED TO THE NEAREST SUITABLE AIRPORT; ELECTING TO KEEP THE AFFECTED ENG RUNNING SINCE THE CHECKLIST DID NOT REQUIRE SHUTDOWN.

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#2 ENG OIL PRESSURE BEGAN FLUCTUATING FROM 100 PSI - 150 PSI; WITH AN ENG OIL LOW PRESSURE LIGHT FLUCTUATING CORRESPONDING. THE #2 OIL QUANTITY INDICATED 0. OIL TEMP WAS NORMAL (130 DEGS); AND THE ENG WAS RUNNING NORMALLY. DECIDED TO DECLARE AN EMER AND DIVERT. NORMAL APCH AND LNDG ON RWY X. DID NOT SHUT DOWN ENG UNTIL ARR AT GATE. ENG WAS SMOKING AT GATE DUE TO OIL LEAK ON HOT SECTION OF ENG. SUPPLEMENTAL INFO FROM ACN 795787: THOUGH R OIL PRESSURE INDICATIONS WERE ABNORMAL; THE CHKLIST ONLY DIRECTS A SHUTDOWN OR RETARDING TO MINIMUM THRUST REQUIRED WHEN EXCEEDING 'RED LINE LIMIT' OR 'LOWER AMBER BAND' RESPECTIVELY. AT IDLE THRUST ON THE GND; THE R ENG OIL QUANTITY INCREASED TO 4 QUARTS. FIRE TRUCKS FOLLOWED US TO GATE WITH NO EXCHANGE OF INFO. I SECURED THE R ENG DURING THE NORMAL PARKING SEQUENCE ONCE AT THE GATE. WHEN WE OPENED THE COCKPIT DOOR; AFTER ACCOMPLISHING THE PARKING CHKLIST; A FIRE CHIEF WAS THERE TO GREET US. HE INFORMED US THAT THE R ENG WAS SMOKING EXCESSIVELY DURING TAXI-IN. SURE WISH SOMEONE HAD INFORMED US OF THIS SITUATION. DOES THE ARPT FIRE DEPT HAVE THE CAPABILITY TO COMMUNICATE WITH THE COCKPIT DIRECTLY? IN ZZZ1 DURING THE PLANNING PHASE OF THE FLT; WE KNEW WORK HAD BEEN DONE ON THE R ENG RELATED TO THE OIL SYS. THE #4 BEARING SCAVENGE LINE HAD BEEN REPLACED DUE TO EXCESSIVE PRESSURE (200 PSI). ALSO; THE #5 BEARING COVER HAD BEEN REPLACED DUE TO HIGH OIL CONSUMPTION.