Oiled birds often suffer from hypo or hyperthermia. Many haven't eaten in days and are often dehydrated by the time they are captured. They must be stabilized before attempting cleaning. Stabilized birds have a much higher survival rate than birds that are not stabilized prior to being washed.
Stabilization usually consists of feeding, fluid therapy and rest.
Most birds can safely be held as much as 5 days before being cleaned. In the United States we use DAWN dish-washing liquid. In other countries we use similar detergents that have been proven safe to the birds and effective on removing oil from feathers. The time varies depending on the size of the bird and the amount of oil on it. Obviously a heavily oiled pelican or penguin will take much longer to wash than a lightly oiled duck or gull.