Burnt oil on food and cooking pans can be bad for you and your health if you eat it or breathe it in.
The fumes from the smoke of the burnt oil certainly are not good to breathe in and if you do experience smoke from burnt oil in your kitchen turn on your range hood exhaust and also open windows and doors if possible to let the smoke out.
I've had smoke from cooking in my kitchen and as soon as it starts smoking up in the kitchen I open windows and the back door to let the smoke out.
My kitchen is at the back of my house that leads out to a patio so I open the door and let the smoke out.
If it's nice weather I try to leave that back door open when cooking to help get rid of any cooking smells.
Burning food or burnt cooking oil also releases chemicals which can lead to lung issues and possibly lung cancer so it's best to avoid breathing that in as much as possible.