The oil is known as lanolin
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.
Black sheep normally turn gray as they age. Normally a ewe's fleece will get dryer and coarser and sometimes their wool will fall out in places especially if they're bred every year.