On close inspection, though, Sefer Vayikra in fact has a simple, elegant, and meaningful structure. The stories and laws are closely integrated into thematic sections. Basically, there are three halachic passages in Vayikra. Each of these comes right after a story, completing the story and memorializing the lessons learned from it. And the three sections themselves seem to fit a quite interesting pattern, which will be discussed later on.
The stories and laws can be summarized as follows:
|(Shemot 25-40||Story 1: The Mishkan is built)|
|Vayikra 1-7||Halacha 1: Sacrifices in the Mishkan/Temple|
|Vayikra 8-10||Story 2: Nadav/Avihu killed at Mishkan inauguration|
|Vayikra 11-24:9||Halacha 2: Establishing boundaries|
|Vayikra 24:10-24:23||Story 3: A blasphemer is put to death|
|Vayikra 25-26||Halacha 3: The Sinai covenant and fear of God|
(I ignore chapter 27 because I consider it to be completely outside the basic structure of Sefer Vayikra - see here.)
This reacts to the previous story (in Sefer Shemot) in which the Mishkan was built. Now we have a Mishkan, this tells us what to do with it. The Mishkan was only constructed once, but the use or maintenance of the Mishkan, by means of these sacrifices, was supposed to continue forever.
This is the first story actually in Vayikra. The Mishkan is inaugurated through an intricate procedure. But meanwhile, Nadav and Avihu bring an incense offering which God hadn't commanded, and they are killed for this offense.
Nadav and Avihu's crime was to offer incense which God had not commanded. More fundamentally, they failed to recognize that the Mishkan is especially holy, God's special territory so to speak, and different rules apply there than elsewhere (see here). Their crime was to ignore the boundary between the Mishkan and regular life.
As a result, the laws which follow the Nadav and Avihu story are all about establishing boundaries between the holy and the non-holy. Specifically, between kosher and not-kosher food, purity and impurity, holidays and regular days, priests and everyone else, and the Temple and outside life. Even the non-ritual and social-justice laws in this section (chapter 19, parshat Kedoshim) are presented in terms of preserving the distinction between holy and non-holy. Nadav and Avihu's failure to recognize the distinctiveness of the Mishkan is used as an opportunity to emphasize the distinctiveness with which Jews must conduct themselves throughout their lives.
A man is caught blaspheming God and is imprisoned. God says that he should be stoned to death, and they do so. God also specifies the punishments (capital or monetary) for various other crimes.
Sefer Vayikra begins with the introduction, "And [God] called to Moshe, and Hashem spoke to him from the Tent of Meeting, saying...".
This implies that first laws in the book were given not on Mount Sinai, but in the newly built Mishkan. The same seems to be true of all the laws which follow it, until chapter 25 (parshat Behar) - the beginning of the "Halacha 3" section. Here, the command is introduced with the line "Hashem spoke to Moshe on Mount Sinai, saying...". Apparently the "Halacha 3" section was in fact given at Sinai, while “Halacha 1” and “Halacha 2” were not.
If we look at the details of this final section, we see further links to Mount Sinai. Parshat “Behar” includes laws of the sabbatical year, the jubilee, slavery and the land, as well as a brief discussion of idolatry, Shabbat, and the Temple. All of these are very similar to the laws in parshat Mishpatim, which is the main body of laws following the Mount Sinai story. The next chapter, “Bechukotai”, is even more closely related to Sinai. It is the text of a covenant, and the only covenant which has been made so far is that of Sinai.
But at the same time, “Halacha 3” differs from the previous stories from Mount Sinai. There, it seems that humans can function somewhat autonomously and independently from God, though of course not in rebellion against Him. Here, the constant repetition of the phrase “ani Hashem”, and the symbolism of God as ever-present ruler and owner, indicate a different theological perspective. While the mitzvot in "Halacha 3" are like those in Mishpatim, the tone seems to be more like the rest of Sefer Vayikra.
As R' Yoni Grossman says, at Sinai we accepted the Torah willingly - out of love of God. Love is an extremely important aspect of our relationship with God, but so is fear of God. This equally important second face does not play a major part in Mishpatim, presumably because it was not what motivated us at that point. But it is the main aspect here. If fear of God had only been presented in connection with the Mishkan, earlier in Sefer Vayikra, we might mistakenly think that fear of God is only relevant in certain ritual contexts. In fact though, it is necessary in every aspect of our religious life. Thus the commitment of parshat Mishpatim and Mount Sinai is essentially "repeated" here, this time with fear not love as motivation.
Now, finally, let us return to the story of the blasphemer, which precedes these laws. On one level this is simply a story of sin and punishment - the exact details do not matter - which parallels the blessings and curses which follow two chapters later. The knowledge that death sentences are actually carried out is a deterrent against performing capital sins.
On another level, this particular story is thematically connected to the Mount Sinai experience and especially to parshat Mishpatim. It is the first story of a judicial death penalty in the Torah, in contrast to the many previous stories in which people are killed miraculously or without due process. It thus represents the institution of the judicial system which is implied by many of the laws in Mishpatim. The unusual digression in God's declaration of punishments is even more suggestive. After the punishment for blasphemy (the only immediately relevant law), God specifies several other punishments. Murder is punished by death, killing an animal is punished monetarily, and injury to a person is punished "eye for eye, tooth for tooth". These laws are virtually word-for-word the same as their parallels in Mishpatim. The overall impression is that in this story, the laws from Sinai are being implemented for the first time.
And in summary...
It is worth noting that there are exactly three sections in Sefer Vayikra. It is even more interesting to note the progression of the sections: first a section directly related to the Temple service; then a section establishing boundaries, related to the Temple but also relevant outside it; then a section with no connection to the Temple, designed simply to impress fear of God upon us and reconnect to the Mount Sinai experience.
This progression has two striking thematic parallels. The first parallel is the division between the sectors of the Jewish people: kohanim, leviim, yisraelim. The second parallel is the three-tiered physical structure of the Temple itself. In both cases, as in the structure of Sefer Vayikra, there are "higher" and "lower" degrees of sanctification, and a third non-ritual level in which we must nevertheless behave strictly according to God's commands.
It seems that Sefer Vayikra is intentionally designed to suggest one or both of these parallels. Through observance of the various types of laws in Vayikra, we can form our entire society into a kind of Temple. Even today when some fraction of the laws are inapplicable, through the remaining laws we can nevertheless make our community into a vehicle for God's presence.
We also learn - as a general guide for religious life - that ritual laws must be coupled by ethical laws and vice versa, and both types of laws must be underpinned by fear of God.
Interestingly, Sefer Bamidbar seems to have exactly the same story-laws-story-laws pattern as Sefer Vayikra. The difference, of course, is that in Bamidbar the stories are much longer and dominate the book, while the laws are subordinate to them.
UPDATE: Kiddushin 33a mentions that Torat Kohanim, the midrash on Vayikra, is divided into "thirds". Perhaps this is the same as my three-part division? Doubtful, but still...