You don't get to "charge" anyone. A public official can be sued to perform their job, and in limited situations, you may sue the employer for that official's neglect (subject to various tort claims acts).
Your recourse is through the legislature, and your political party.
There are several very good constitutional lawyers in town. Perhaps you'd like to invest in a few hours of their time, and they will gladly teach you how all the issues in your question fit together. The law schools may also have a course on constitutional law that you could audit.
Only prosecutors can charge people with crimes. Normally, if you feel an election law is unconstitutional, you would bring a lawsuit seeking to enjoin the unconstitutional practices. If you win, you will get an injunction requiring the state officials to follow the court ruling. However, I am not aware of any section of the constitution requiring any sort of oath by a candidate for office. After being elected, the winner takes an oath of office, not that he is qualified, but that he will faithfully discharge the duties of his office. You can read the entire constitution at http://www.findlaw.com/casecode/constitution/ then identify the provision you believe is being violated.
If you feel that a candidate is unqualified, you can file suit in federal court seeking to have a judicial ruling that the candidate is not to be allowed on the ballot. Such a lawsuit will lose in virtually every case, because of the inability of the complainer to prove that the candidate is unqualified, but you can always try anyway.
Contact me at 248-399-6930 for a free consultation. You and I do not have an attorney-client relationship formed by our communications on this website. Advice given by me on this website is general advice based on partial information. You should not rely on any advice given without first hiring a lawyer in the area where the case is pending, and providing that lawyer with full information.