I think 油をあける is not standard Japanese. Standard Japanese is 油をすてる So, the writer use a direct although I never heard of it before. Or the writer is not a native Japanese and she translated EMPTY into 空ける akeru. We use 空ける like ボトルを空ける。empty a bottle

「油をあける」means “remove cooking oil from a pan”. So 「フライパンが十分温まったら、油をあける。(その後)、バター(またはサラダ油)を入れる」means “ When you heat the pan enough, remove the oil from the pan. And then put butter in the pan.” When you cook something on a non-Teflon-coated iron pan, you should do “油をあける” not to burn ingredients. (Put cooking oil in the pan, heat the pan and then remove the oil from the pan: we call this process “油ならし”). But recently most people use a Teflon-coated pan because ingredients don’t get burnt soon on the coated pan. So you don’t have to do the process of “油ならし” when you use the coated pan. That’s why many people don’t often use this expression “ 油をあける”. But you may find it in some recipes(especially in the recipes of Chinese food). まあこの表現を覚えておいて損はないですよ^_^

I think it's not a usual expression in that sentence but if you say あける, it means to empty up the container. So in such case, it should mean to put all the oil prepared for stir frying(usually it should be 1 table spoon) into the frying pan. And for the fist sentence, you can use either butter or oil, but not both.