What forms are needed to fill out after overstaying on visitor visa to get a green card?

Generally, when a foreign national has entered the U.S. lawfully and with inspection (it sounds like this may be true for your mother-in-law), has a U.S. citizen child age 21 or older (it sounds like this may be true for your wife), then the adult child may sponsor the parent in an adjustment of status application process in the Immediate Relative visa category. This is true regardless of whether the foreign national may have overstayed her initial visa. Through this process the foreign national may become a Lawful Permanent Resident (get a "Green Card"). That application process involves such forms as a Petition for Relative Alien form, Biographical Background forms, an Affidavit of Support form and an Application for Adjustment of Status form. With this families generally also file an application for an employment authorization document and (when eligible) an application for advance parole. Proper completion of each form can be more complex that it appears, and the necessary supporting documents vary from case to case. There really is no substitute for your family members to consult with an immigration attorney who, after learning all of the relevant information, could advise about eligibilities, options and strategies to attain your family's goals, and who then could offer legal representation in the often complex application process.