A 2003 study published in Lipids journal compared the impact of emu oil, fish oil, flaxseed oil, and olive oil on inflammation and found emu oil to have the greatest anti-inflammatory properties. The results echoed the findings of a small Vancouver study, which showed that men with burned skin treated with emu oil healed better than the control groups.
Since many skin conditions like eczema, psoriasis, and acne involve inflammation, it makes sense that emu oil's anti-inflammatory qualities could provide benefits for people who suffer with these conditions. Emu oil is noncomedogenic, meaning that it doesn't clog pores, so people with acne need not fear the oil will make the situation worse.
If, instead, dry skin is the bane of your existence, emu oil is an effective emollient that is able to penetrate the surface of the skin without leaving a greasy residue. Emu oil also traps water, which might be useful if you are trying to reduce the appearance of fine lines and wrinkles.