Add a thermostat to the TT circuit on the oil burner relay, set it where you want the minimum temperature of the house to be. When the wood fire dies the house will drop temperature until it reaches where this thermostat is set then fire the oil burner and the oil burner will hold that temp in the house until you relight the fire.
If you do not get domestic hot water from the oil burner set the low limit on the aquastat down to 120-130, this will allow the cirulator to start pushing heat sooner when the wood fire is coming up. Do not change the high limit as this should be the design temperature for the system to keep your house warm on the coldest days.
With this simple set up it will also allow the oil to fire when the weather is really cold and the wood fire cannot keep up with keeping the house warm.
I set the 2nd thermostat on my system about 4 degrees lower than the main thermostat.