In reply to Fraser:
Another thing that might be worth trying but will require real care...
Get an iron and some brown paper or possibly just heavy duty kitchen roll.
Place the brown paper/kitchen roll over bit of the jacket that has grease on and put iron on top for a few seconds. If the fabric with the grease on is in contact with any other bits of the jacket place a towel in between - you don't want to spread the grease any further.
Basically, you should be able to heat the oil/grease up and get the brown paper to absorb it. As the grease gets soaked into the paper move it along so you have fresh paper over the greasy bit and repeat.
The caveat is that you need to be really careful you don't burn the fabric though so start with as cool an iron as possible.
I'd try the less risky approaches first!