No impeachment neccessary since he was never eligible to hold the office.
In this case I think they give Biden the oath of office and escort Obama out of the White House.
I don't see how they can. Obama/Biden was a package deal. You couldn't vote for one without the other.
On the other hand, if Biden were to be declared ineligible, I don't think it would invalidate Obama's presidency.
It would be a tough call. Personally, I think the presidency goes to Pelosi.