The fact that the adoption was finalized two years ago pretty much means you're on the hook unless she re-marries and her new hubby chooses to adopt them. Of course the state is "nailing" you for support. Legally these are YOUR kids and you should be supporting them not the tax payers.
I'm sorry your marriage didn't work out but that is not the fault of these kids. You were a part of the adoption process and took that responsibility by signing the paperwork and swearing infront of the courts. It wasn't an option to change your mind if your wife kicked you out. You could have fought for custody but it sounds like you never loved them to begin with which is clearly why many of our foster youth feel unloved and valued for the income they bring in not the love and stability a loving adult wants to offer.