En route to Dallas, Texas, USA, one of the engines began losing power as a result of oil exhaustion. The pilot decided to divert to Austin Airport. The approach was not properly executed and the aircraft eventually ran off the wet runway. The reason for the oil exhaustion was not found. The aircraft had received an annual inspection the day before. PROBABLE CAUSE(S) personnel – maintenance,servicing,inspection: inadequate maintenance and inspection miscellaneous acts,conditions – oil exhaustion-engine lubrication system pilot in command – improper IFR operation pilot in command – failed to initiate go-around FACTOR(S) pilot in command – lack of familiarity with aircraft airports/airways/facilities – airport conditions: wet runway weather – rain miscellaneous acts,conditions – poorly planned approach miscellaneous acts,conditions – not aligned with runway/intended landing area miscellaneous acts,conditions – hydroplaning on wet runway