The herb closest in flavor to oregano is probably marjoram, which is in the same family. It is subtler, though, and lacks the in-your-face aromaticity of oregano.
The difference between oil of oregano and oregano oil is nothing! One can use both types and the terms are interchangeable. Oregano oil or oil of oregano are great additions to cooking.
No, substitutions will change the flavor. While the dish may still taste good, it will not taste like rosemary.
If you are referring to oregano-infused oil, it is most common to use olive oil. But there is such a thing as pure oregano oil (pressed from oregano), but that is a nutritional supplement and not typically used for cooking.
It won't give the same flavor, at all. Parsley is very mild and not very aromatic. You might want to combine it with oregano, thyme and/or marjoram to get more flavor and aroma.
Oregano
Species: Origanum vulgare (oregano).This is the species most often associated with the culinary arts. It is also called Italian Oregano or Greek Oregano. The cultivar, hirtum is a common one. However, there are several species and many cultivars and varieties. Oregano is also a medicinal herb with several applications.
The most common use of the spice oregano is in Italian foods such as spaghetti and pizza.
oregano
The Tagalog name of oregano is "dahon ng oregano."
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oregano