I've seen a lot of somewhat colourful rhetoric recently regarding Mr Obama's comments on Brexit, so I thought I'd add my two penneth worth.
1) You and me (the people of Britain) get to decide if we stay in or out, so whereas it's got bog all to do with him, isn't it useful information to know how the rest of the world is going to react depending which way we go? Personally I'm happy to know beforehand that our special relationship will not extend to trade deals with the US if we exit, rather than assume we'll get them and then find out we're stuffed in that direction.
2) Does he have a right to comment on what we do in Europe? Well most of are making lots of comments about Trump and Clinton...I think it's this idea of free speech that we have, so yes, I'd say he has every right to voice his opinion.
3) Was it all staged by the Stay campaign? Yes, almost certainly, but that doesn't necessarily make any of the points he made less valid.
4) America wouldn't stand for the lack of sovereignty? What do you think each State in the US does to the Central US government?
So, I'm not trying to sway you to vote one way or another, but please also don't let a knee jerk, "who the F*** does he think he is?" reaction sway you either. Listen to all the evidence, opinion and the bullshit and if you decide you can make an informed decision, vote for what you think is right.