[AmericanVictory]

If someone with standing were to file a suit in federal court challenging the eligibility of Ted Cruz, would any of the state court cases which you mention establish a res judicata that would be binding on a federal court?

[Nero Germanicus]

I am not an attorney so I am only stating an opinion, but my undersanding is that res judicata (claims preclusion) can only apply to civil or criminal court actions with the same parties. So a suit challenging Senator Cruz would have no relationship to any of the Obama challenges other than possibly as precedent.
Perhaps an attorney will answer your question definitively.