Why exactly does the Torah forbid sexual actions such as incest? R' Elchanan Samet explains (near the bottom) that the sexual prohibitions are necessary in order to preserve the correct relations between different members of the family. If you are allowed to look at your family members as sexual objects, you may be unable to deal with them in the proper manner (as mothers or sisters or whatever). When the sexual option is made impossible, you are forced to respect them and relate to them as the close relatives, loved and respected, which they are. Eliminating the sexual option with these people thus makes possible a whole range of valuable and necessary family relationships.
I cannot decide to my own satisfaction whether or not this argument is correct. (For one thing, the punishment of death and/or extirpation seem pretty serious for a purely utilitarian law, though there are parallels such as the punishment for cursing parents.) If true, however, it would go a long way towards solving the anomalies of this part of Sefer Vayikra, as can be seen in the following examples.
1) The most striking difficulty with the sexual prohibition passages is that they include several non-sexual prohibitions. Right in the middle of chapter 18 is a commandment not to deliver your son to the "Molech" (18:21). In chapter 20 the Molech prohibition appears again (20:2-5), and there is a double prohibition (20:6 and 20:27) against consulting an "Ov or Yidoni" (i.e. magical communication with the dead). What are these non-sexual crimes doing right in the middle of the sexual crime laws?
The obvious halachic problem with Molech worship, and I believe also with Ov/Yidoni, is that they are idolatrous. But among the types of idolatry mentioned in the Torah, these seem to be unique in that they involve members of your family. Molech worship obvious involves your son, and Ov/Yidoni presumably focuses on your ancestors. In this they are similar to the sexual crimes, which also involve your family.
Assuming as before that the purpose of the sexual prohibitions is to protect the family, it is easy to see why Molech worship is included with the sexual sins. Killing children on a routine basis is, after all, quite damaging - obviously for the children involved, and it probably leads to unhealthy attitudes towards the other children (you're next!) and towards other people in general. Just as a sexual relationship with your mother would prevent you from treating her as mothers deserve to be be treated, the possibility of child sacrifice might prevent you from treating your children with the attitude they require. Therefore both are forbidden in the same passage.
Similarly, I think we can explain why Ov/Yidoni is included with the sexual prohibitions, but first we must look at the final mention of Ov/Yidoni in our parsha.
2) The prohibition of Ov/Yidoni appears once again in close proximity to the sexual prohibitions (in the "kedoshim tihyu" section, verse 19:31). It is immediately followed there by the command to "rise before the aged, and honor the elderly" (19:32). The juxtaposition of these two laws seems odd, but there may be a deep connection between them.
The Ov/Yidoni is an attempt at communication with the dead, and the dead are simply elderly people who are so elderly that they have died. In general, we are commanded to respect and perhaps seek guidance from those people who have the wisdom of age, who bear the tradition, and who created us and supported us when we were younger. At the same time, we are equally commanded not to "pervert" this respect by apportioning it not to our elders, but to their elders who are no longer alive. If we do so, given the inherent meaningless of "communicating" with ghosts, then all the social benefits of respecting the aged are lost. Prohibiting Ov/Yidoni may therefore be a means of promoting the correct kind of relationship with our elders, while excluding self-serving "relationships" based on magical incantations and alleged paranormal instructions from above. This idea is supported by Devarim 18, which contrasts sorcery (including Ov/Yidoni) and true prophecy as possible sources of guidance.
If so, then it is easy to explain why Ov/Yidoni is included among the sexual laws. Just like the sexual prohibitions make it possible to have meaningful relationships with family members of the opposite sex, and the Molech prohibition helps preserve the correct attitude towards one's children, the prohibition of Ov/Yidoni promotes the proper attitudes one should have towards one's elders. Apparently no human relationship is danger-free, and for virtually every member of family and society there must be a law channeling your relationship with them in a constructive direction.
3) The lists of sexual prohibitions are very male-centric. Granted, a woman can figure out that "you shall not uncover your mother's nakedness" prevents her from consorting with her son. But in a literal sense, the prohibition is addressed only to the son. Assuming as before that the purpose of sexual laws is to protect meaningful relationships within the family, we can explain the focus on men in terms of what men and women tend to look for in sexual relationships. Men are more likely to pursue purely their lusts without making any emotional commitment; since these relationships are not stable or meaningful the Torah emphatically restricts them. But women tend to demand emotional commitment in any sexual relationship they enter. If it were up to the women, then even incestuous or unnatural relationships might not necessarily destroy the family. Thus, the prohibitions as a rule focus on men and not women.
4) This model also helps in explaining various notable details among the prohibitions. Don't put me down as having encouraged lesbian marriage, but it seems that the Torah does not prohibit it explicitly because it would be more likely than homosexual male marriage to lead to a stable and successful family structure.
5) More strikingly, exactly one prohibition (bestiality) is separately addressed to women, in both chapters 18 and 20. A woman might be inclined to form a meaningful relationship even with a family member, and thus does not need to be warned against meaningless sexual relations with him. But she certainly cannot form a meaningful relationship with an animal. In this one case, the woman as well as the man must be warned that the relationship is forbidden.
Nearly every line of this post includes a dash of conjecture, and I'm not absolutely convinced that any of it is correct. But it does seem to move a number of verses from the "totally inexplicable" to the "reasonable conjecture" category. That in itself is a reasonable accomplishment, even if final proof will have to wait until some other time.