There's no such thing as a "legal" Presidential candidate. "Running for President" has no constitutional existence.
Also, state election officials would have the right (I think) to have Obama prove his eligibility before they allowed his name on the ballot in their state.
Obama won't be on the ballot in any state. US citizens will be running for the positions of electors for President and Vice President. If you could prove that an elector pledged to Obama did not meet the criteria for the position, you could take THAT to a court.
But before the electoral college meets, these candidates have no actual legal existence.
by law, the Secretary of Homeland Security identifies who he considers "major candidates," and they are entitled to protection 120 days before the election. I could see the Secret Service requiring a named candidate to prove he's eligible to the presidency (what I meant by "legal") in order to continue receiving protection.
"Running for President" has no constitutional existence.
No, but it can still be recognized as existing by federal law in the case of Secret Service protection. "having no constitutional existence" doesn't necessarily mean "unconstitutional."
Obama won't be on the ballot in any state..., etc...
Technically true, but the party's nominee's name is always on the ballot along with the party's name. I don't know why election officials in Michigan, for example, couldn't refuse to display Obama's name next to the "Democratic Party" spot on the ballot, if he couldn't prove his eligibility to the presidency.