Is transitioning to all electric heating smart?
First step is to convert those prices into something you can compare on equal footing.  $0.063042/kWh = $17.50/GJ, for oil, $2/gal = $13.7/GJ

So, superficially, oil is cheaper than electricity for the same amount of energy.  However, there are a couple of other things to consider.


Oil combustion is only about 75 - 90% efficient at heating because you have to exhaust the products of combustion, losing some heat in the process. 
Electricity on the other hand, when converted directly to heat (like in a baseboard heater, or electric furnace) is 100% efficient.  
Electricity can be used to run a heat pump which, instead of turning the energy source directly to heat, uses a refrigerant to move heat from outside, allowing you to get 2 - 3 GJ of heat into your house for every GJ you put into the heat pump.  This GREATLY improves the cost effectiveness of electricity... but....
Heat pumps typically have a minimum temperature at which they will operate effectively.  This temperature will depend on the model and they are getting much better, but you may still have to depend on resistive heating on the coldest days of the year.  


Given your assumptions, the prices you have thrown out, it seems like it will be a wash, or slightly cheaper to use electricity.  Long term reliability, equipment costs, and other concerns may be a different story, however.