I am a US Citizen, can I apply adjustment of status for my parents who over stayed but entered with a valid VISA?

Why was their case denied? They were not supposed to leave the US if their case was filed under 245i. They would not be eligible for adjustment of status now if they left the US and reentered. Only if they can prove that they entered the US lawfully in 2008 (it is doubtful that it was really lawful with that AP document since they were not supposed to use it) can they apply for LPR status through you now. Be very careful, however, because the whole thing is likely to come up and they can be subject to removal. Please let me know if you have any additional questions or how I can be of further assistance to you in this matter.

Your question requires an attorney consultation. It is not a simple question that can be answered on this type of forum. There are many factors that would need to be considered and evaluated. I strongly suggest that you contact an experienced immigration attorney for a face-to-face consultation and give him/her all of the facts surrounding your situation. He/she would then be in a better position to analyze your case, advise you of your options and, if possible, make sure that the necessary paperwork and documentation is presented so as not to delay the process.

Looks like they'd be subject to the 10 year bar, which would be lifted in 2018. They can only be eligible to apply for a waiver if there's a qualifying relative who will suffer extreme hardship. That relative cannot be you. Generally, it has to be a U.S. citizen or permanent resident spouse or parent. There may be other issues stemming from their prior attempt to legalize. You should speak to a lawyer.