I would say already damaged not caused by the oil although I have no idea what angular leaf blight is.
Strelitzias are very tough and will survive most things. How much of a plant have you got left? If their are plenty of leaves I would cut off the damaged ones to the base. It will soon put up fresh ones. I take it you have freshened up the soil or repotted? They do like to dry out between watering and if possible put it outside for the Summer. Somewhere shaded from the hottest part of the day. Nature will soon take care of any spider mite left and it will benefit from being out of an enclosed environment. I put all my houseplants outside for the Summer including my now 10 year old Strelitzia.
Having just reread your post you don't actually say what zone you are or if it is potted or you can grow it outside.