As reported to the FAA. Reports are unverified, and codes are left as the FAA publishes them.
What was found
WHILE PARKED AT THE FBO, THE CREW NOTICED A SURGE IN THE APU, THE ACFT LOST ELECTRICAL POWER FOR A MOMENT, THE APU RECOVERED, ELECTRICAL POWER RETURNED, THEN THE CREW NOTICED THE OIL ODOR AND SMOKE IN COCKPIT. THE CREW THEN SHUTDOWN THE APU FOR FURTHER TROUBLESHOOTING.