AN MD80 GEN OIL PRESS LOW LIGHT ILLUMINATED AFTER TKOF. THE ENG WAS SHUTDOWN WHEN THE GEN DID NOT DISCONNECT. AN EMER DECLARED WITH A DIVERSION TO A NEARBY ARPT.

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SHORTLY AFTER TKOF FROM ZZZ; L GEN OFF LIGHT BEGAN CYCLING. SHORTLY THEREAFTER L GEN OFF LIGHT CAME ON STEADY. I BEGAN RUNNING THE L GEN OFF LIGHT CHKLIST; THROUGH COMPLETION TO TURNING ON THE APU. SHORTLY AFTER THE CSD OIL PRESSURE LOW LIGHT ILLUMINATED; SO I BEGAN RUNNING THAT CHKLIST; WHICH CALLS FOR ACTIVATING THE CSD DISCONNECT SWITCH. A NOTE IN THE PROC SAYS TO CONFIRM CSD DISCONNECTED BY OBSERVING VOLTS AND FREQS. FREQS WENT TO ZERO; BUT VOLTS REMAINED APPROX 115; WHICH LED US TO BELIEVE THE CSD WAS NOT DISCONNECTED. I AGAIN HELD THE CSD DISCONNECT SWITCH IN THE DISCONNECT POS. STILL HAD FREQS SHOWING. THEN THE CSD OIL OUTLET TEMP INDICATED OFF SCALE HIGH. ALL STEPS IN THE CSD OIL OUTLET TEMP HIGH PROC HAD ALREADY BEEN ACCOMPLISHED. WE DECIDED TO CALL MAINT CTL FOR SOME INPUT; AS WE FELT THE CSD WAS STILL TURNING. CAPT SPOKE WITH THEM ON THE RADIO WHILE I HAD THE ACFT. HE REPEATED THEIR INPUTS THAT ENG DAMAGE WAS A POSSIBILITY AND WE SHOULD SHUT DOWN THE ENG AND LAND. WE EXECUTED THE INFLT ENG SHUTDOWN PROC; WERE APPROX 30-40 MI AWAY FROM ZZZ1; SO DECLARED AN EMER WITH INTENT TO LAND ASAP AT ZZZ1. WE WERE ABLE TO GET DOWN VERY EXPEDITIOUSLY THANKS TO CTR AND APCH. IN OUR HASTE TO GET ON THE GND WE WERE A LITTLE FAST GOING THROUGH 500 FT; IE; DID NOT MEET THE STABILIZED APCH CRITERIA; BUT WELL UNDER CTL ON GS FOR RWY XX; VREF WAS 137; AND WE TOUCHED DOWN AT APPROX 145 KTS. LANDED OVERWT (133.5) WITH A SMOOTH TOUCHDOWN. THROUGHOUT IT ALL WE SHOULD HAVE PROBABLY TAKEN AN ADDITIONAL 270 OR 360 TO LOSE ALT TO BE MORE STABILIZED FURTHER OUT ON FINAL. CAPT DID AN OUTSTANDING JOB HANDLING THE ACFT THROUGHOUT; WITH EXCELLENT SITUATIONAL AWARENESS.