The Underground Is one system operated by Transport for London. Originally it was all underground when it was just in central London only. But as it began to expand out into the suburbs at the end of the 19th century, it wasn't put underground where there was land still available so it could be built on the surface. Why tunnel if you don't have to? It's cheaper and far easier not to! So in fact over half of it isn't underground - pretty much almost everything outside fare Zone 2 is on the surface. (The obvious exception is Heathrow Airport, where it had to go under the airport.) But the name sticks. Once everybody knows it, it's hard to change.
The Overground is a much more recent renaming of some National Rail lines that are entirely inside London, to make them look more closely like part of London's transport and hopefully get the message over that the ticketing arrangements are the same - fares are the same and you can use Oyster. There are National Rail trains within London as well that will also take Oyster, but the Overground, unlike those, is firmly in the hands of TfL so TfL could name it as it wanted.
Southeastern is just one of the train operating companies that operates trains in the rest of the UK. Don't necessarily expect that within London, you can use Oyster on it - mostly, on that and the other national rail operators that come into London, you can, but check to make sure. You certainly can't pay with Oyster for going outside London except to Gatwick.