I can't answer the hot water heating so easily. But do not go with your current plan for space heating.
TL;DR If you're going to switch to electric heat, get a modern heat pump.
With some unusual exceptions, most modern (last 100 years+) space heating systems for small buildings are one of the following:
- Burn fossil fuels to heat water, transport hot water throughout the building
- Burn fossil fuels to heat air, transport hot air throughout the building
- Electric resistance heaters in individual rooms
- Electric resistance heaters to heat air, transport hot air throughout the building
- Use electricity to pump heat from outside to inside (exact reverse of air conditioning which pumps heat from inside to outside)
The first system (you have a variant of that) is one of the older types (though modern versions are available). It has the advantage of working with minimal electricity (thermostat, controls, etc.) or possibly no electricity at all. If powered by oil, it has the advantage of being self-contained (no natural gas supply needed). But there are disadvantages too, and they are gradually disappearing.
The second type is extremely common in the US, generally powered by natural gas piped in via a utility. This can produce a lot of heat very quickly (feels great!), but generally requires a natural gas line or a propane tank. The air handler requires a moderate amount of electricity, but not all that much, and the air handler also doubles as part of an air conditioning system in the summer. These systems have become more efficient in recent years, with new systems more than 90% efficient.
The third and fourth systems are almost the same. Electric resistance heat, whether simple baseboards, room-size units with fans, portable plug-in heaters, or whole-house systems connected to ductwork (which from the user perspective are little different from natural gas furnaces), is also nearly 100% efficient in converting electricity to heat. This seems ideal (until heat pumps) except that are significant losses in producing electricity (which is often from fossil fuels) and in transmitting electricity long distances. As a result, the cost effectiveness of oil (usually boiler) or gas (usually forced air) heat vs. electric heat has varied over the years and by location. Where electricity is relatively cheap (typically in nuclear or hydro areas), electric resistance heating can be less expensive than high-efficiency gas heating. Where electricity is more expensive, burning the fuel locally with an efficient system will generally cost less.
The last type is the newest. Heat pumps have been around for a long time, basically as long as air conditioning. Actually, modern refrigeration is really a miniature heat pump, but except for big commercial units (walk-ins) with the heat going from the inside of your refrigerator to your kitchen (great in winter, not in summer).
The beauty of heat pumps is that they have become incredibly efficient, and the hardware is not that much more complex than an air conditioner. A heat pump works both directions (heat in to out and out to in) instead of the single direction of an air conditioner (heat in to out). Older heat pumps did not handle relatively cold weather very well, so they come with "emergency heat". That emergency heat can be a full natural gas furnace, but unless you already have that in place, the usual solution is electric resistance heat because it is very low cost to buy and install.
In the old days, heat pumps were not used much in northern parts of the US because they could not handle cold weather (e.g., 20s F) very well. When the outside temperature gets too cold, a heat pump won't work well (if at all) and falls back (typically) to the relatively expensive to run electric resistance heat. If you need that emergency heat a lot of the time, there is little point in bothering with a heat pump as a natural gas furnace will cost less to run.
However, today's more efficient heat pumps (a) can handle much colder temperatures, so the emergency heat is rarely needed if the right system is installed for your climate, and (b) have gotten so much more efficient that they not only save a lot of money when running than electric resistance heat, but they save a lot of money (=power, fossil fuel, CO2 emissions, etc.) compared to the old standard of high-efficiency natural gas furnaces.
"electric oil filled radiators" produce a more even heat than "giant toaster baseboard heaters". But the power in/out is exactly the same. Which is 100% efficient for direct electricity usage but far less efficient compared to moving heat from outside to inside.