3rd Aliya: The deaths of Nadav and Avihu are recorded at the very same time that fire descended from heaven to light the Mizbeach. Their cousins removed the bodies of Nadav and Avihu from the courtyard of the Mishkan. Moshe instructs Aharon and his two remaining sons, Elazar and Itamar, that they are forbidden to overtly mourn the deaths of Nadav and Avihu in the standard manner. It is from here that we are taught the standard practices of tearing Kriyah and of mourners not cutting their hair.
4th & 5th Aliyot: Moshe instructs Aharon and his sons to continue the service of the Mizbeach's consecration. The first recorded difference in Halachik rulings is recorded between Moshe and Aharon as it pertained to the eating of the Rosh Chodesh offering. (Note 16-20, Stone Edition ArtScroll pg. 595)
6th Aliya: The basic laws of Kosher and non-Kosher animals, fish, and fowl are recorded. Note that verses 11:4-7 is one of the established proofs for the divine authorship of the Torah.
7th Aliya: The basic laws of purity and impurity are recorded. It is important to clarify that the Torah does not associate "Tummah" impurity and "Taharah" purity with good and bad. The entire process involves the concept of life and death and the symbolic emphasis that the Torah places on serving G-d with optimism and vigor. So long as there is life there is the opportunity to grow in our relationship with G-d.