Here begins Paul's massive argument. He begins talking about the Gentiles (though, as I said, slyly about the Jews as well). Their sin is simple: the way the world is made leads logically to the idea that it was, well, made. To ignore that and thus deny God is foolish. That leads them to their sin. Though this passage is often cited in debates about whether or not "those who do not know the Gospel" will go to heaven or not, this really has nothing to do with that. In context, all Paul is saying is that they had a chance to at least acknowledge there is a God. If they miss that, then they've missed the boat and God gives them over (1:24, 26, 28) to what they want. As Lewis says in Problem of Pain, the lost "enjoy forever the horrible freedom they have demanded, and are therefore self-enslaved."

1:26-27 is referring to homosexuality. Paul mentions it because no Jew or Roman would argue with him that such sexuality was "against nature" and disgusting. However, Paul turns the tables on his audience when he lists sins that would be more commonly held as common and acceptable. "Disobedient to parents"? Well, sure everyone does that. But he sticks it right up there alongside homosexuality.

Romans 1:18-32