Can I apply for change of status and LPR if I am out of status?

Generally a foreign national must be in valid nonimmigrant status in order to be eligible to apply to adjust status to become a Permanent Resident. There is an exception to this rule for a foreign national who entered the U.S. lawfully and with inspection, and then applies to adjust status as a spouse of a U.S. citizen - this is true even if the foreign national's initial visa may have long expired. It would be wise for you and your wife to consult with an immigration attorney who, after learning all of the relevant information, could advise about eligibilities, options and strategies to attain your goals, and who then could offer legal representation in the often complex application process (such as helping your wife succeed with a naturalization case at the earliest possible time and helping both of you with an adjustment of status application).