A main reason storage is useful with wood boiler hot water heating is that, as opposed to your oil boiler which can turn itself full "on" in seconds and then full "off," a wood boiler has a load of wood to burn whether or not your system needs the heat. The btu's from that burning wood have to go somewhere, and a storage tank is an ideal place to put them. The wood boiler too can shut down, but the shut down is slower than with the oil boiler, and the wood boiler too can restart, ditto. But unlike the oil boiler that efficiently starts up and shuts down by controlling the fuel supply, the wood boiler does the same by controlling the air supply. That is inefficient at best and increases emissions in the start and stop cycles. Ideally, wood burns best when it burns without interruption from start to finish under the controlled air conditions of your Eko.
There is no single answer to how much storage you "need." I believe your Eko is designed to work with no storage, with inefficiencies. So you don't need any storage. The next level of "need" is enough storage to handle the excess btu's from a load of burning wood. You can control that to a considerable extent, and therefore have minimal storage, by timing and sizing your wood loads to more accurately supply only the heat you need, with the minimal excess then going to storage. But that also will require more frequent tending and monitoring the wood boiler operation, which greatly will depend on heat demand, outside temperature, etc. Not the most convenient but very workable.
Maybe the highest level of reasonable "need" is as large as could handle the btu's from a burn of a full load of wood with no demand from your system. Let's say that is 100 lbs. of wood, which is about 500,000 btu's (6050 btu/lb at 20% MC, 400F stack temp, and 85% efficiency for the boiler). If your minimum useful system temperature is 150F, and your boiler is capable of 190F output, then 1500 gallons of water could handle that (1500 gal x 8.34 lb/gal x 40 delta-T). 1500 gal is probably more than most users with storage have.
Need then also relates to how long you want to be able to provide btu's from storage to meet system demand between boiler firings. To deal with this you need to know your heat loss, that is, how much heat you need to maintain the interior temperature you want for comfort. You need to do a heat loss calculation to determine this, or estimate it from experience. Let's say that is 50,000 btuH. In the last example, with 500,000 btu's stored and heat loss at 50,000 btuH, storage could provide 10 hours of heat before the boiler would need to be fired again.
Although this is complicated at the extreme, others users can chime in with their practical experience and provide a user's guide as to the amount of useful storage for an Eko 40. I have a Tarm Solo 40 (140,000 btuh rated output) and have 1000 gal of pressurized storage. Works very well in my situation with heat loss maximum at about 20,000 btuh and minimum usable temperature of 100F, and I can store 750,000 usable btu's.
No - you cannot use oil storage tanks for pressurized storage. Don't try it.
I assume your current oil boiler system is pressurized, the Eko 40 is pressurized, and I would recommend staying with pressurized storage if at all possible. In my mind this is simpler and more efficient, but also due to space considerations doesn't work well for many people.
Others will have more to add. Enjoy your system. Don't fret too much.