The abomination (the worship of foreign Gods) was committed long before the angels got there.<quoted text>
God smote all the men of Sodom with blindness as they attempted to beat on Lot's door and break in and commit abomination with the two male messengers. They were not blind from birth.
A wise man looks to multiple sources for his information. Jewish folklore talks about Sodom and the problems that it had. That cry to God? Described as a woman who had been covered in honey and hung from the city wall so that wild bees would devour her as punishment for her crime. The "crime" that she committed? She fed a traveler that had been beaten and robbed by the citizens of Sodom. After he was beaten and robbed, the townsfolk refused to feed him, refused to provide a court of law for him to accuse his attackers (c.f. Genesis 9:6).
While this IS just the folklore explanation, it DOES fit with what is written in Ezekiel...
Ezekiel 16:49 Behold, this was the iniquity of thy sister Sodom, pride, fulness of bread, and abundance of idleness was in her and in her daughters, neither did she strengthen the hand of the poor and needy.
16:50 And they were haughty, and committed abomination before me: therefore I took them away as I saw good.