This subject is covered in great detail elsewhere. I will give a very brief description of the most up to date and scientifically correct methods. For more detail, contacts and a downloadable manual, visit Removing Oil from Feathers- a link to California's Oiled Wildlife Care Network.
There are some strange ideas around on how to get oily products out of a bird's feathers. At no stage should petroleum ether or sand be used. Nor should a bird be put through the wash when it first arrives.
The first things to look for when the raptor arrives are hypothermia and dehydration. Because they rely on their feathers for insulation, an oiled bird can't control it's body temperature. You will have to do this with a heated enclosure, and regular monitoring to make sure the bird is not overheating. Dehydration can be corrected as with any other injured bird. Also remove any oil or other grime from mouth, eyes and nares. Then leave the bird to recuperate.
If the bird is weak, DO NOT attempt to remove the oil. The washing procedure is very stressful, and may kill a shocky raptor. With oiled sea birds, professional teams monitor the birds' blood chemistry to see when they are recovered enough for this. It may be several days, and after they have been fed several times. In some cases where the oil is toxic, the birds are also given medicine to help remove this from their digestive tract. Preventative medication for infections is also given to birds who are badly affected.
When the raptor has recovered it's strength, and has been allowed to put on a little weight if it was starving, it is time for the wash. In some cases, this may be the day it was brought in, if it wasn't in the oil too long. Even then, it should spend a couple of hours being quiet and warm, and be given fluids to make sure it is hydrated. At least two people are needed to do the wash, even on small birds. One holds and monitors the bird, the other washes.
Several big tubs should be set up ready, with ordinary dish washing liquid concentrate added to hot water. If the oil or tar on the feathers is thick, pre-treat with very warm vegetable oil. Rub it in to soften and liquefy the gunk, then remove as much as possible with towels. This will alow the detergent to get in and lift it off better. Water temperature should be very warm, to keep the bird from getting cold, as well as softening the oil. Remember that birds have a higher body temperature than us, so what feels medium to luke warm to us is COLD to a bird.
A hood is a great tool to reduce the stress on the bird while it is being washed. Place the bird in the first tub, and gently start rubbing the oil off, making sure to rub in the direction the feathers grow, or you will damage them. Work methodically over the whole body, trying to get every feather clean. When one tub of water gets greasy, move on to the next. This is where a third person is useful in getting the baths ready. For light oilings, two to three tubs of detergent water should get all the oil off. The last baths are plain water, as a rinse. You will need more than one rinse to remove all the detergent, and once this happens, you will be able to see water starting to run off the feathers. Raptor feathers do not cause water to bead, and they do not rinse dry like seabirds or ducks. Clean feathers are water repellent, even without the preening oils the bird spreads on them.
This type of procedure should get all the oil off a light to medium oiled bird within an hour. If it is a very thick oil, you may have to do a second wash after the bird has had a few days to recover. At any point, if the raptor shows signs of laboured breathing, excess stress or hypothermia, finish with a rinse and let the bird recover, even if all the oil isn't out. The raptor should be returned to it's heated enclosure to warm up and dry. Make sure this is a well ventilated space, so that it takes less time for the bird to dry out.
After all the oil appears to be out of the feathers, and the raptor has recovered from the stress and any other problems it may have had, test it's water resistance with a light mist spray, sprayed onto the bird for a minute. Alternatively, check the bird when it rains- be prepared to bring it in if water is getting through to the skin. Water should bead up and roll off of the feathers on all parts of the bird.