What exactly to you want to know? About the second example: I think you hit the nail on the head. Here's how the Longman Dictionary of Contemporary English defines "oversight":
o‧ver‧sight / ˈəʊvəsaɪt $ ˈoʊvər- / noun [ uncountable and countable ]
1 a mistake in which you forget something or do not notice something : I assure you that this was purely an oversight on my part.
2 have oversight of something to be in charge of something : He has general oversight of all training courses.
Definition 1 applies to "It was through an oversight than you were not invited.".
Student or Learner