Are individual electric heaters more efficient to operate than an electric boiler?
To answer the main question, an electric boiler is exactly as efficient at turning electricity into heat as individual electric heaters. However, individual electric heaters allow per-room heating setups; if you only rarely use a room, you can turn the heat down. However, an oil boiler will almost always be cheaper to run than either, unless you live near a nuclear power plant or dam. (Although an oil delivery is expensive, you don't need oil delivered that often.)

However, with this specific property, having a central boiler, plus a fireplace insert, plus individual heaters, tells me that the central boiler is probably not able to keep up with the heat demands of the house. (Side note: relying on a fireplace for heating is a terrible idea. They leak most of their heat to the outside, and add a large draft to the house.) It sounds like the house was made when it was expected that people would wear a sweater while indoors during winter, with the house not being heated to "room temperature". So, the individual heaters were added in order to provide an extra boost, but comfort is still not going to be great, and you'll probably be paying a lot for heating unless you're willing to use the sweater method.

My suggestion would be to keep the boiler for now. Those things have a service life, and you might as well let that service life run out. In the meantime, you should upgrade the sealing and insulation of the house to at least close to modern standards. This will increase comfort and decrease heating load.

(Side note: some houses have in-ground oil storage. These are expensive to deal with, and you do not want that. Make sure you know where the fuel oil is stored.)