I am not a particularly good painter but used oils for many years before converting to acrylics about 4 years ago.
You can use oils as thin washes and I found them more controllable than acrylic, they flow better, although I may not have found the right flow agent yet. Very often I get run back with acrylic washes which I never got with dilute oils.
Because they have a long drying time you can mix paint on the figure as well as the pallet to get a more even blend. The current fashion for the tri colour system is I think because the paint drys so fast is hard to blend. Bear in mind most of my painting recently has been in Greece in the summer, it's hot and acrylics go off very fast.
As Svenn mentioned if you put oil on thickly and then wipe it off you get a very nice shade and highlight. Usually this would be over white undercoat to provide the highlight. I found old flannel bedding worked well to wipe off with a soft material with a bit of a nap.
Horses are good for this technique but it works well for other things. Blues are good for faded jeans, leather and fur are also good this way.
Using a green undercoat and then a very dark brown coat wiped off is good for a dark African skin colouring
Most oils will stay workable on your pallet much longer than acrylics.
The big downside is that drying time can be days or weeks and you will smear the paint job if you touch it, dust also becomes a problem as well.
I changed systems because I had to pack everything away after a session and stuff had to be dry to handle.
Note using thinners with the oils means drying time are quicker, but still problematical.
Let us know how you get on.