As I recall when we did oil boilers at plumbing school, there are two types of oil used in oil burning boilers:
28 sec - this is the most common (I have it at home) and it is called kerosene or paraffin.
35 sec - this is a heavier oil and is not so common in boiler/heating applications because of the flueing requirements. It is also known as red diesel or derv, it is basically diesel with a red dye additive and another invisible chemical marker to catch out people who do not pay their duty.
You are asking if you can use a 35 sec substitute (cooking oil) in a 28 sec application (your boiler). I would think that at the very least the jet on your Sterling burner would need changing, probably even the pump and then you would need to have the flueing checked to make sure you would not suffer the effects of Carbon Monoxide poisoning.
There are burn anything oil boilers you can buy, they are mainly used for burning used engine sump oil. And they do burn very, very cleanly - so cleanly that they let them install one inside (tahts indoors) the international building show in Hannover, Germany.
However, if the reason you are asking is because you can get copious quantities of veggie oil consider a two boiler setup. In short, just nail a second (35 sec) boiler to the wall and away you go. It may sound daft, but you are better off having two small boilers rather than one large boiler - one for heat the other for water - you do not need a 70,000 BTU boiler whanging out enough heat to power a nuclear sub when all you want is a bath full of hot water.