I support just_ace comment. Oil out the back exhaust is usually over fuelling, fuel passing through unburnt attached to the carbon produced from combustion (looks like oil but is fuel and carbon).
Usually to fix means a tune (1990 means checking your air/flow sensor setting, tps setting, getting injectors cleaned, cleaning throttle body, n/a timing (cams on n/a is more prone to fuel out the exhaust due to cam timing overlap), spark plug replacement, upper head clean spray (wrx dealership), service, warm car / reset ECU / restart car, dyno tune (if you want to throw money at it to be perfect).
Unless you are loosing lots of oil (dipstick level), your issue is just a tuning one :) to do with fuel.
Smoke under acceleration is good (to a point) as it means your not lean!