Any detergent will act as a surfactant in the dye bath which is why you add it to the bath. You only need a few drops particularly if you are using a household detergent. Too much and you will get a lot of suds Woolite & Synthrapol are also very good and low sudsing. The materials ought to be as clean as possible before going into the dye bath. Again, most any detergent will work and warm water will also loosen oils. Soaking hair overnight will help open the pores so they will take up the dye a bit faster and deeper.
Ostrich will not take high heat well so keep an eye on the dye bath temp. The barbules are very fragile and will curl easily. Polar Bear hair will take heat but the skin could be damaged with excessive heat. Long & low heat on these substrates is best. Keep agitating during the dying process and keep feathers & fur off the bottom of the dye pot where the heat is highest. At high heat (boiling), the protein in the feathers & fur become almost liquid (not like water of course) to the point that deformation can occur (curl). Solid hair like Polar Bear takes dye slowly and I find that a more concentrated dye bath makes a better dyed hair. Feathers take up dye quickly.
For very greasy skins you can soak them in paint thinner and it will leach much of the oil out. A couple good washings after that treatment will get rid of the odor.
There is a book by AK Best called "Dying & Bleaching Natural Fly Tying Materials" and he gives a pretty good overview of the process.
You can use regular Hydrogen Peroxide & water at a 50/50 mix to bleach feathers & fur. Too long tends to damage though so keep an eye on it. The beauty shop strength bleaches are quite "hot" and can get away from you if you don't watch them closely. Any of them also dissolve protein to some degree and the hotter strength can dissolve the skin. A few drops of detergent won't hurt as a surfactant here as well.
It is wise to do tests of the dye before putting your materials into the bath. This is particularly true if you are blending colors. Just use a feather or in the case of Ostrich, a barb or two to see what the final color will be. The colors look darker when wet so you will have to dry them to see the actual color. A hair dryer will facilitate this.