Birds are the species that are very quickly impacted as they depend so much on their feathers to protect them from the environment. Some sea birds never come on shore except for during the breeding season, and their feathers are exquisitely designed to protect them from the cold water and provide buoyancy.
When a bird comes in contact with oil, and that can be just a very small amount, the oil damages the structure of the feathers. Feathers provide a cosy, waterproof cocoon in which the bird is protected from the cold and the heat. The trapped air in the feathers provides buoyancy and allows them sit comfortably on the water surface.
They maintain the integrity of their feathers by regular preening, this involves‘combing’ the feathers into position, allowing the tiny hooks to line up and the result is the water simply bounces off the body(see first video below) When they come in contact with oil, it seeps into the feathers and damages this structure, as a result the coat is no longer resistant to the water and the water seeps in to the skin (see second video below).
A birds body temperature is much higher than a human and they quickly use up their body condition trying to stay warm. They also stop hunting for two reasons, they are busy preening trying to recover the integrity of the feathers and because they have also lost their buoyancy and are struggling to stay on top of the water.
Because they cannot hunt they not only loose body condition but they also become dehydrated as they depend on their food to provide water. Birds will struggle but if they do not drown or die from the temperature(either hot or cold) they will eventually beach themselves(or jump onto the nearest thing that takes them out of the water) to avoid the cold.