For a job that relies heavily on genealogy, the sons of Aaron are largely background players in the book of Exodus. A lot of that has to do with Aaron himself; as the high priest, Aaron is the one in charge. His sons will eventually take on that mantle (literally), but right now, the focus is squarely on Aaron.
Unless your name is Nadab or Abihu, that is.
From the time that I was a kid, I remember hearing about Nadab and Abihu. They’re probably most well known for offering “strange fire” before the Lord and dying on the spot (Leviticus 10:1-2). It’s a dramatic scene that drives home the necessity of doing things as ordained by God.
But that’s not their only appearance. In fact, we first see Nadab and Abihu in Exodus 24:1, when God tells Moses to bring them alongside Aaron and the seventy elders to meet God on the mountain. Eleazar and Ithamar, who are full blood relation to Nadab and Abihu (they share the same mother and father according to Exodus 6:23), aren’t invited.
As the oldest, Nadab and Abihu should have been next in line to take over the high priesthood from Aaron. Instead, their failure means that Eleazar, the third oldest of Aaron’s sons, becomes high priest after Aaron (Numbers 20:25-28).
Before taking that role, Eleazar serves a variety of positions. He’s the one responsible for the daily operations of the Tabernacle (Numbers 4:16), as well as retaining the responsibility as the “chief of the leaders of Levi” (Numbers 3:32).
Not only would Eleazar himself serve with distinction during the time of Moses, but his son Phinehas was also a model of integrity. When Balaam (the guy who talked with a donkey) led Israel into sexual immorality, it’s Phinehas that grabs a spear and kills the offenders when everyone else sat on their hands (Numbers 25:6-13).
Ithamar is perhaps the least well-known of Aaron’s sons, but that’s probably because he occupies virtually no Textual real estate outside of his brief mention in Exodus 28. His primary responsibility seems to be the transportation of the Tabernacle (Numbers 4:25-32). Because there’s no evidence of his disobedience (like Nadab and Abihu), it’s assumed he served honorably.
Like most genealogies in Scripture, the focus is on those who carried the story further, not on providing every tiny detail we might like to know. The focus with Aaron in Exodus is on the establishment of the priesthood. It makes sense that those around him are discussed in relation to their devotion to that institution.