jonathan396
Does the plug have 3 or 2 prongs?

It’s from 2011. This post is almost 10 years old since the last time anyone interacted with it.

wasn't sure where to add the oil

jonathan396
I got my delonghi oil heater about ~15 years ago. Just found it again recently after not being used for a while and it started making a high pitched sound when I woke up.

Nah, I think you should keep using it until it explodes and starts a fire while you are asleep.
 
I don't have any idea why anyone would buy and oil-filled heater in the first place.  It is purely resistive heating.  It is no more efficient that the conventional resistive heaters which are cheap and can't explode.