British style guides require the period inside; American style guides require the period in the location that relates to the actual stop (i.e., inside if it is part of Obama's speech and outside if it is a part of the matrix sentence.)
Or I may have those guidelines reversed. Anyway, I use the latter.
Ellipsis + period is 4 dots, but if the sentence does not end, I would put the period outside. Still, I think that most editors would eliminate both ellipses as unnecessary.
When I looked at this last time, I think I found that the style in several national British newspapers (at least) is to put the period inside if the quote that ends the sentence is a complete sentence in itself, otherwise outside. Your example seems like a complete sentence, so the period would go inside. On the other hand, in the following, the period would go outside: