Does pork fat oil give an off taste?
I wouldn't describe it as an "off taste", for me it is the tasty flavor of pork fat, commonly known as lard. But yes, it is certainly not taste neutral. It only gives a slight to moderate hint in baking (e.g. in pie crust) and gets really strong when you heat it more, e.g. when you fry in it or baste a roast. 

For a comparison of the smell, think bacon.