Even if Obama was definitively found to be ineligible for office, that would not automatically void any of the laws or executive orders he has signed. This is due to a legal concept called the "de facto officer doctrine", which has been recognized by the Supreme Court.
IMO the defacto officer doctrine would not apply to Obama, he has been challenged on his eligibility before he took office and it is not just a perfuntory administrative challenge.
the SCOTUS can be replaced too, think outside the box