There are only 130,000 -150,000 adoptions, total, annually in the USA. That in itself makes it impossible that there are "hundreds of thousands of children given to sodomites each year," even if all the heterosexual mom-and-dad adoptive parents were in fact sodomites.
As reported in the U.S. Census, in 2012, 110,000 children, total, were living with gay parents. Of these, an estimated 65,500 children were living with their natural parent (genetic father or mother) and a gay "spouse" who had also adopted the child. In other words, one natural parent and one adoptive parent.
Gay and lesbian parents are raising four percent of all adopted children in the United States. So, based on, say, 150,000 total annual adoptions, that would be 6,000 LGBT adoptions per year. Not "hundreds of thousands."
Different agencies would have different reporting methods or different definitions, and thus end up with somewhat different totals, but none of them vary much from what I just quoted. Here's where I went to get the info: # of children adopted
I do not in any way approve of LGBT couples adopting children. I am convinced that it violates the child's natural right to be raised by his father and mother. I just wish to point out that it does your argument no good to use absurdly inflated statistics.