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I actually did some googling and there are some okay-ish articles debating this topic. All of them said “it depends”, which isn’t really helpful.
It got me thinking, though… how much savings would you need to make it worth it to you? ($20 savings? $100 savings? $500 savings?)
The oil heater is going to cost ~$50 to purchase if you don’t already have one. That means you’ll at least need to save $50 just to break even. So over the winter, your electric bill will need to drop by $50 plus whatever the dollar amount you need in order for it to be “worth the trouble” for you.
If an extra $50 over the winter in savings ($100 total) is worth it to you, I think you have a high chance of an oil room heater getting you that savings over your central heating. I’m doubtful how much more you’d be able to save beyond that. (I didn’t do the math on it, but based on the articles I read, the oil heater is going to be cheaper in general.)
Another thing to consider: The oil heater is likely to be a lot more convenient to use than the central air option and having to close all the other vents in your house though.