What is an Orthodox Christian parish? Is that like eastern orthodox religion? Or would it be considered a conservative nondenominational Christian parish?
An Orthodox parish is the same as what is called a “congregation” in protestant denominations. If you see, for example. a “Holy Trinity Orthodox Church” in your town or city, that is a parish with its priest(s), members, and building, etc.
Perhaps you can find an English-language Orthodox parish near you, and experience Orthodox worship for yourself!