The oil is known as lanolin
its called a fleece
A fleece
Sheep grow wool. When the wool is shorn from a sheep it is called a fleece.
The word you're looking for is 'fleece'.
fleece
Wool is spun from the fleece of sheep.
because the wool contains lanolin
because they give off an oily/fatty substance called lanolin.
With electric shears - they used to shear them with hand shears
After you cut a sheeps fleece you will want to wait at least six weeks for the new coat to grow in. You may choose to wait longer for a thicker coat, but do not cut the sheeps fleece any sooner than six weeks.
It really isn't oil. It's lanolin.
The fleece of a camel is called camel fleece. If it is mixed with sheep's wool, it is called camel hair.