I think one can find sodomy as SIN even before the Ten Commandments were given.
Genesis 18:20-21
20. Then the LORD said, "The outcry against Sodom and Gomorrah is so great and their sin so grievous
21. that I will go down and see if what they have done is as bad as the outcry that has reached me. If not, I will know."
Genesis 19:4-7
4. Before they had gone to bed, all the men from every part of the city of Sodom--both young and old--surrounded the house.
5. They called to Lot, "Where are the men who came to you tonight? Bring them out to us so that we can have sex with them."
6. Lot went outside to meet them and shut the door behind him
7. and said, "No, my friends. Don't do this wicked thing.
20 And the Lord said: The cry of Sodom and Gomorrha is multiplied, and their sin is become exceedingly grievous.
21 I will go down and see whether they have done according to the cry that is come to me: or whether it be not so, that I may know.
22 And they turned themselves from thence, and went their way to Sodom: but Abraham as yet stood before the Lord.
23 And drawing nigh he said: Wilt thou destroy the just with the wicked?
24 If there be fifty just men in the city, shall they perish withal? and wilt thou not spare that place for the sake of the fifty just, if they be therein?
25 Far be it from thee to do this thing, and to slay the just with the wicked, and for the just to be in like case as the wicked, this is not beseeming thee: thou who judgest all the earth, wilt not make this judgment.
26 And the Lord said to him: If I find in Sodom fifty just within the city, I will spare the whole place for their sake.
27 And Abraham answered, and said: Seeing I have once begun, I will speak to my Lord, whereas I am dust and ashes.
28 What if there be five less than fifty just persons? wilt thou for five and forty destroy the whole city? And he said: I will not destroy it, if I find five and forty.
29 And again he said to him: But if forty be found there, what wilt thou do? He said: I will not destroy it for the sake of forty.
30 Lord, saith he, be not angry, I beseech thee, if I speak: What if thirty shall be found there? He answered: I will not do it, if I find thirty there.
31 Seeing, saith he, I have once begun, I will speak to my Lord. What if twenty be found there? He said: I will not destroy it for the sake of twenty.
32 I beseech thee, saith he, be not angry, Lord, if I speak yet once more: What if ten should be found there? And he said: I will not destroy it for the sake of ten.
The other two groups in Genesis apparently don't mentioned.