If it was applied as normal practise without sealing the wood so that the oil penetrated the wood well then I suspect you are not going to remove it without as the previous post intimated mechanically cleaning off the infused wood.
Unfortunately there is no real way of removing Osmo Oil because it is designed to ingress into the wood.
With it being an oil you can try sanding it off but I'm afraid you may end up loosing the detail and thickness of the wood. As mentioned painting is probably your best option.
Just had a similar problem when a client changed her mind about the colour part way through a project. Mylands dewaxing solution instantly stripped it straight off. Even though it was oak no stain remained, even in the grain.Makes me wonder how deep osmo oil really penetrates.