An important post this - I cannot emphasise enough how seriously you should take carbon monoxide.
Carbon monoxide risks are often thought to mostly affect gas and solid fuel range cookers but oil cookers can also produce carbon monoxide if operating incorrectly.
The first thing to say is that servicing, as with all appliances, is crucial. All range cookers, except electric, need to be serviced/checked at least yearly. They were often installed many years ago so things like flues and chimneys should also be looked at every now and again - your flue MUST be lined for example and cannot simply go into a chimney.
In between this though what happens if something goes wrong? Firstly your pets will be affected first. They are smaller and are akin to the canary in the coal mine. If your dog starts sleeping a lot more than usual that can be a sign of CO poisoning - see this story.
To make sure you know the minute there is a problem you absolutely MUST have a CO alarm in the kitchen. You can buy many alarms, from £25 or so upwards, but this is not something to be cheap about.
I reccommend, unreservedly, Nest alarms. They are owned by Google and combine a clever fire alarm (won't be triggered by kitchen accidents!) with a CO detector. Are they a little more expensive, yes. They cost just under £100. They are worth it for the following reasons.
I own 4 NEST alarms across home and office and all are connected to my phone along with two NEST cameras to let me keep an eye on what is going on. Worth. Every. Penny.
I don't sell NEST alarms just go buy one now from Amazon - you will not regret it!