In the Chalcedonian Churches, the ordained orders currently in use (in ascending order of rank) are that of Reader, Subdeacon, Deacon, Priest or Presbyter, and Bishop. Readers and Subdeacons are so-called "minor orders", the others "major orders". There used to be other minor orders, such as Doorkeeper and Chanter, but these have largely fallen into disuse. The minor order of Taper-bearer has been subsumed by that of the Reader. One cannot exclude the female diaconate from this list: although it disappeared completely for a time, there are a small number of female deacons (or deaconesses) active today in the EO Church. It should be remembered, however, that while the female diaconate and the male diaconate are usually considered to together form a united order (the diaconate is more often considered to be one, not two) deaconesses do not have much of a liturgical role to play.
One should be careful about speaking about which order is more senior than another (even though this is of course a perfectly legitimate distinction to make), since each order, especially when speaking of the major orders, is considered "full and equal". That is to say, they all have their function in the body of the Church and together with the laity manifest the Church in its fulness in each local community.
Titles of function and honour given to clergy can make things pretty confusing for those not familiar with such things. A hieromonk or priest monk is a monk who is a priest. A hierodeacon or monk deacon is a deacon who is a monk. "Archpriest" is a title of honour given to a married priest. "Protodeacon" is a title of honour given to a married deacon. "Hegoumen" and "Archimandrite" (Archimandrite being higher) might be titles of honour given to priest monks, or they might denote genuine authority as an abbot in a monastic setting. "Archdeacon" is a title of honour given to a monk deacon. Some jurisdictions bestow the mitre usually worn by bishops on certain senior Archpriests. All of this can be confusing, because Slavs, Greeks, Romanians, Antiochians etc. might have these titles and more,and have them mean different things.
I believe non-Chalcedonian Churches have evolved in a slightly different way when it comes to Holy Orders. Posters from these Traditions will have to answer your questions about their ordained ministries.