What do the Old Testament Apocrypha and Pseudepigrapha say about homosexuality?

The Revisionist Answer
This body of literature does not read the Old Testament passages as condemning homosexuality in general; rather they refer to some other sin, such as pederasty. Sodom is condemned for its pride and inhospitality.
Even if homosexuality is understood to be the sin of Sodom, this interpretation is wrong and linked to the sin of the angels before the Flood. These angels committed a sin “against nature.” In turn, this interpretation in the Apocrypha and Pseudepigrapha has wrongly influenced various places in the New Testament (Jude 7; 2 Peter 2:6–8) so that they also link the sin with that of the fallen angels. All of these improper connections arose in the intertestamental literature because of Jewish aversion to Greek homosexual practices.

The Traditional Jewish and Biblical Answer
Various passages in the Apocrypha (Ecclus. 16:8; 10:13–18; 49:2) use such terms as abomination and arrogance—terms associated with homosexuality—to describe the sin of Sodom. 

Wisdom of Solomon 14:23–26 cites “confusion of sex” as one result of idolatry; this phrase may be rendered, “interchange of sex roles.” Wisdom 19:13–17 and 10:6–9 describe the sin of Sodom as inhospitality, as well as “ungodly,” “wickedness,” “failure,” and “folly”.

The Pseudepigrapha even more definitely associate homosexuality with Sodom. Second Enoch 10:4–5a and 34:1–3 use stark language to describe sodomy. Third Maccabees 2:3–6 describes the Sodomites as acting “insolently” and becoming “notorious for their crimes.” Jubilees 7:20–21, 16:5–9, and 20:5–6 describe the sin of the Sodomites as “wicked,” “sinners exceedingly,” “defiling themselves,” “committing fornication in their flesh,” “working uncleanness on the earth,” “fornication and uncleanness,” and “pollution of sin.” Fourth Ezra 2:8–9; 5:7 and 7:102–31 refer to Sodom as coming under divine judgment. 

Testament of Naphtali 3:4–5 and 4:1 refer to the sin of Sodom as “wickedness” and that which “changed the order of nature” in a way similar to the sin of the angels before the Flood. Testament of Asher 7:1 connects the sin of Sodom with that of the angels. 

Testament of Benjamin 9:1 refers to the “fornication of Sodom.” Testament of Levi 14:6 refers to “the union” of Sodom, and 17:8 refers to unmentionable “pollution.” Levi 17:11 makes the only reference to pederasty in all of the Apocrypha and Pseudepigrapha, associating pederasts with adulterers, the arrogant, and those who practice bestiality. Other Testaments refer to “revolting gentile affairs,” “the evils of the Gentiles,” or “corruption in fornication.” The Letter of Aristeas 152 indicts gentile men for, among other sins, having “intercourse with men” and “defiling their own mothers and even their daughters”.

The intertestamental literature is frank, not only in associating homosexuality with Sodom, but also in denouncing this as an evil gentile vice. The view of Sodom and its sin flows out of a plausible interpretation of the sin of Sodom found in the Old Testament itself and of the homosexuality described in Leviticus 18 and 20 as “abomination” or “detestable.” This literature does not distort the Old Testament. If certain New Testament passages reflect the terminology of this literature, they do so because this literature accurately reflects the sin of Sodom and the homosexuality of the nations that is prohibited in Leviticus.