Greek shortening has a different taste than shortenings you might find in your market. If you aren't happy with the taste and/or quality of the results using other shortenings and Greek shortening isn't available, try this trick to deliver a better end result:
Add a little butter (salted or unsalted, depending on the recipe) to cooking oil. The amount of butter will depend on the taste of the oil. A starting point would be a ratio of 4 to 1 (for example, 4 teaspoons of oil combined with 1 teaspoon of butter).
Margarine is a reasonable substitute.
This mix of oil and butter gives a sweeter result. In Greek cooking, shortening is often used to sauté, to add moisture to roasted meats, and in baking.