What are the natures of the different "priesthoods" mentioned in the old testament In the old testament, there are three (maybe more?) references to a priesthood.


  Genesis 14:18 Melchizedek king of Salem brought out bread and wine. (Now he was the priest of the Most High God.) 19 He blessed Abram, saying, “Blessed be Abram by the Most High God, Creator of heaven and earth.


This was also referenced in reference to Jesus:


  Hebrews 7:17 For it is declared: You are a priest forever, in the order of Melchizedek.


The second is of Jethro, Moses' father-in-law:


  Exodus 2:16 Now the priest of Midian had seven daughters; and they came to draw water and filled the troughs to water their father’s flock.


And finally the priesthood of Aaron ordained by God through Moses.

Are these all referring to the same priesthood? If they're different, what sets them apart from each other? Are they all priests in some fashion for God? The first two intrigue me the most as I know next to nothing about them.

Thank you!
The first order, the order of Melchizedek, is controversial. You can search this site, and especially see this question. 

The Hebrews 7:17 reference is actually quoting from Psalm 110:4, which is a prophecy about Jesus, that he would be a priest in the order of Melchizedek.

I liked Mason Wheeler's answer on that question, which in part stated (emphasis mine):


  [T]he Order of Melchizedek is a higher order of priesthood than the order of Aaron, which the Levites operated under. It had the power of administering the "schoolmaster law," but not the full power and authority of the higher ordinances of the Gospel, and so by the Aaronic order alone, nothing could be made perfect. But the order of Melchezidek, which predates the Aaronic order, is the priesthood order of Christ himself.


Also, from Wikipedia:


  Abraham's transfer of goods to Melchizedek is seen to imply that Melchizedek is superior to Abraham, in that Abraham is tithing to him. Thus, Melchizedek's (Jesus') priesthood is superior to the Aaronic priesthood (who are descended from Abraham), and the Temple in Jerusalem is now unnecessary.


Whether you believe that Melchizedek was Jesus, or merely a "picture of" or a foreshadowing of Jesus, he is named as a priest, and clearly a highly ordered priest.

As to the priesthood of Jethro, the picture is not as clear. This article makes the argument that he was indeed a follower of the God of Abraham, Isaac, and Jacob. After providing the background, it states that:


  Jethro was the priest of deity El, whose name was isolated and new name, taken up as Yahweh by Moses. Jethro is not a pagan priest, but the priest of the deity whose ancestors of Moses worshipped. This patron deity is now revealed to Moses as Yahweh, He is who He is, He was who he was and He is who He is to be.


However, two Jewish sources (here and here) state that he was a Pagan priest, who later renounced his Pagan gods. Evidence of this is given in Exodus 18:11, when Jethro says:


  Now I know that the Lord is greater than all other gods, for he did this to those who had treated Israel arrogantly.


The second article addresses this by explaining the situations surrounding Moses' meeting his future wife:


  Those who are certain that he really was a priest say that having realised that idol-worship was foolish, he resolved to abandon it. He was punished for this heresy; no-one would now keep his flocks, and this is why his daughters were tending the sheep and why the shepherds tried to drive them away.


Maybe the reason you know next to nothing on these two priesthoods is that there are two different views for both of them, and neither can be decisevely stated from scripture which view is correct.

As to the priesthood of Aaron, called the Aaronic priesthood by the LDS Church, and the Levitical priesthood by most others, this is the priest most people think about when they hear the word "priest" in a Bible context. Descendents of Levi, these priests were responsible for sacrifices, teaching, liturgical duties, everything pertaining to the tabernacle and later, the temple, and various other duties within the Israelite/Hebrew people. These two sources (src1, src2) provide an excellent history and summary of the Levitical priesthood.

As to a discussion from an LDS point of view on the differences of the priesthoods of Melchizedek and Aaron, see this question &amp; answer.