Yes they can get greasy via natural oils or greasy hair products. This can be helped by washing them with cold water and using skin products meant to help oily skin.

Teenagers hair and skin may be greasy because of hormones. Hormones cause an overproduction of oil, which also leads to acne.

it produces oils to stop itself from drying out.

The birds skin is a leathery material but when wet starts to feel greasy.

The four main skin types are:

Normal

Dry

Greasy

Combination