LB, to break up your conversation with yourself, here’s some terminology:
In general, when someone says Chareidi, they include both Litvish Yeshivish and Chasidish, and of course Sefardim can also be chareidi.
Litvak means someone coming from Lithuania, Litvish is the adjective. It is used to refer to someone who is not chasidish, even if he doesn’t hail from Lithuania. When chasidus started, mainstream Judaism was very much opposed to the movement, and those who fought against the early Chasidim were called Misnagdim (opposers). But now since chasidus in its current form has been accepted as a halachically valid approach to Torah, the term misnagdim no longer has any meaning, so non-chasidim are called litvaks. The Litvish approach is different from the chasidic one in many ways- too long to go into now.
Chasidus was prominent in Eastern Europe- Poland, Galicia, Russia, Hungary but not where Sefardim lived (Mediterranean, Mid-Eastern, North African countries)- so historically sefardim are not chasidim. Those who are (e.g. there are a lot of Sefardi Breslover Na-Nachs) have adopted a culture and minhagim that are not originally their own. Litvish Sefardim is a contradiction in terms, since they both refer to geographic areas. Sefardim can be chareidi, yeshivish, modern, traditional (mesorati) or anything else.