Unfortunately there are way too many variables just to answer that definitively.

If you put a thousand Watt resistive heater in a room 1,000 watts will generate 1000 watts worth of heat give or take. But if you use a heat pump, 1000 watts of power can be used to move 3,500 Watts worth of heat outside to in. Speaking from a theoretical power concept.

If you're heating your entire house to 20 or 30° above ambient, you'll have losses on the roof in every wall, If you're just eating one room all you have are the losses of that room so insulation becomes a weird thing to calculate.

You can't just let your pipes freeze if you're a freezing zone, but generally unless you're central is super efficient, maintaining a comfortable temperature in one room is more cost-effective, heating one room should cost somewhat less than try to heat the whole house no matter what method you're using.

If you're in an area that doesn't freeze you can keep the house cold and heat one room with an electric oil filled radiator very inexpensively.

If you're in a place that freezes you need to keep the house warm enough to avoid freezing the water pipes.

Otherwise have fun, heat one room and bundle up everywhere else.

Not really an answer to your question, but if you live somewhere that freezes think about where your pipes are.

You gotta heat the bathroom and kitchen and any other rooms that may have pipes running through them, or you’re going to freeze and probably burst some pipes.

Or, you could leave your taps trickling, but that expensive too.

Heating just the room will be overall cheaper. However doing the whole house will be cheaper per square foot because your room isn't insulated against other rooms, just to the outside, so you'll lose a lot of heat to bleed through to other rooms.

Both are just converting electricity to heat which is already a very efficient process. It's unlikely one of them is significantly better at that.

Eating a room sounds expensive. Not just in terms of the materials required, but also paying for the aftermath.

Get a cheap thermometer to place in the room you're going to heat and look how much it is off the thermostat and regulate accordingly.

Leaving one room cold while others are significantly warmer might raise the risk of mold, because the warm air might cool in the cold room and condensate on the walls and windows, creating conditions for mold growth.

I look that every room is at least about 16°C as an absolute minimum in winter.

I'm not familiar with mobile oil radiators, but it sounds kind of dangerous to me.

Just an FYI, closing up vents in an hvac can actually cause problems. It puts more strain on the fan unit, which can cause it to burn up quicker. The unit is designed to move a certain amount of air, if you restrict that air, pressure builds up in the system.

A couple closed over an entire system is fine, but closing all but one room would definitely cause problems.

I'm curious to an actual, scientific answer, but I do something similar, and here's my anecdotal results:

I've got one of those electric fireplaces (fancy 1500w space heater basically) in my den, and I usually spend a lot of time in here (it doubles as my WFH office). I'll turn the central thermostat down about 5 degrees and just run the fireplace while I'm working in there. When I'm done, I'll bump the main thermostat back up.

My furnace is gas, and the price keeps rising every year, but doing this over the last 3 years, my gas bill has stayed relatively flat even though the price has skyrocketed. I think it averages me an extra $20 at most on the electric bill which is less than the gas would have cost.

Granted, I live by myself, so I don't have to worry about other people in other rooms getting chilly lol.

There are far too many variables to know for sure. What fuel does the central heat use? Where is the house built? What sort of sun exposure do you get? What type of house is it? What's in your attic? Basement? How much time do you spend at home during the day?

I would go with the central heat, generally speaking.

Homes are insulated differently depending on where you live, but the exterior walls are usually better insulated than the interior ones. The heat in one room will dissipate to neighboring rooms. You're correct that closing vents will direct the hot air to the desired rooms first. Over the course of the day, some of the energy will disperse and warm other rooms. One space heater might use less energy than your central air, but you will need to run it longer and more frequently.

You may also find that you're keeping the one room hotter because you're always cold in every other room. Getting warm and staying warm are two different physiological processes. Keeping the house at 66 may feel warmer than keeping one room at 72.

Consider what each heat system was built to do. Central air is there to keep the house warm. Central air is most efficient when it is automated to maintain heat. Allowing the space to get very cold every day will cause it to run longer when you feel cold.

Meanwhile, a space heater is a short-term hot spot in a room. It's designed to create immediate warmth in the immediate area. Use it when you are feeling cold to get yourself warm, and then shut it off. If you use each one to do its job, that's probably going to be the most efficient.

The best thing you can do for your energy bill is insulate. Get a temperature sensor, wait for a cold day, bring your entire house up to ~70, and then go hunting for cold spots. Check around window sills and near brick or masonry walls. Airflow through your walls is dollar bills flying out of your wallet. You can place film over leaking windows, replace caulk when it cracks, and fill voids that happen when old insulation breaks down or gets wet. Check your attics and crawlspaces for airflow as well, and consider reflective foil as an inexpensive upgrade if you can get to the rafters.

If everything is properly insulated, all heating and cooling becomes more efficient.

What type of central unit do you have?

Pretty sure any serious answer needs to factor in where there insulation sits. It's not only about heating a space but how much you need to heat continually to keep it warm.

Most all forms of heating are near 100% efficient, since it's the waste heat you want. Unless the central heating is using a heat pump instead. Does your central heating use gas heating? If so, using it will probably be cheaper. If it uses resistive heating, the individual unit might be cheaper. But if it uses a heat pump, it might be cheaper to use central again. There are a lot of variables it's hard to know.

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.

If you're basically living in one or two rooms in an otherwise unoccupied house then the space heater is probably better since you won't have to deal with the thermostat being in another area.

If you're going to need heat in different rooms all over the house then I'd say let the central heat do it's job. You really don't want to deal with running around opening and closing vents and having to warm up another room every time you need to go in there. It will be a pain in the ass and probably cost a lot more.

What kind of unit is the central system - heat pump? Resistive heating?

There are a lot of details we'd need to determine this, so I don't think we can give you a firm answer. But heat pumps are dramatically more efficient than resistive heating, so if the central system is a heat pump that's probably the right answer. If the central system uses resistive heating then it's probably not much more efficient than the small heater.

How cold does it get where you live and which sides are the room and living room on compared to the coldest wind?

If the room you use is on the north side and the cold wind comes from the north, that electric heater is going to get a workout and you lose the advantage of the house having a heat mass that can even out the need to hwat the one room.

If the room is on the south side away from the wind the rest of the house would be a bit of a buffer, making heating only that room less of an energy simk. The number of windows and other ways to lose heat will matter too. If the living room has a lot of windows and other ways to leak heat then not heating it could be an advantage.

If it gets to freezing where you are at I would suggest a combined solution if possible. Set the central heat to a temp a bit above freezing to keep the pipes from bursting (around 55 F) and shut the ducts to rooms you don't care about. The difference in temp to the outside temp is what uses the most energy, and closing that difference has a huge difference on energy costs. Then use the space heater in the room you do care about to reach the temp you want.

This will result in the central unit doing a lot less work than it would to bring the whole house up to temp, but the portable unit wouldn't need to heat the the room and the interior walls nearly as much becuae it would be heating the difference between the central unit at the desired temp. This will probably be the most comfortable/consistent arrangement and likely close in cost to just doing the room by itself.

Tp calculate needs way more info that. U would need to know the effective efficiency of the central heating system. The houses per room insulation effect and inter room insulating effect. The heat output of each device. Ambient temperature. Then u could do some thermodynamic analysis to determine which is more expensive. Alternatively u just measure both taking care to compare the getting to temp and maintaining temp separately.

I believe u thermostats are a standard wiring so u can probably wire up a relay and a raspberry pi with a wireless thermostat.

Do you not plan on using the living room at all? Because the room you're residing in is the one you definitely want to be warm to avoid mold.