I know that there are three cases on this daf and that they concern Kohanim, Nzirim and yisraelim, but I do not understand the connection of the cases to Osek Bamitzvah patur min hamitzva
Jon Oppenheim, Scarsdale, New York
Let me first point out that the D'rashah to which you are referring concerns, not the principle 'ha'Osek be'Mitzvah Patur min ha'Mitzvah', but the Mitzvah of burying a Meis Mitzvah, which overrides it.
Rashi in B'rachos 19b cites the Sifri, which explains the issue as follows:
The Torah has written "Al Nefesh Meis Lo Yavo", incorporating his close relatives, which raises the question why the Torah needs to add 'le'Aviv"?
To which the Sifri answers - that Torah adds 'le'Aviv', to teach us that it is only for a father that the Nazir is forbidden to make himself Tamei, but for a Meis Mitzvah, he is obligated to do so. It then adds 'le'Imo' (which we ought to already know from "le'Aviv"), to teach us that even if the Nazir is also a Kohen (thereby adding to his sanctity) he is nevertheless obligated to bury the Meis Mitzvah;
... "le'Achiv" - even if he is a Kohen Gadol,
... and "u'le'Achoso" to teach us that even if the Nazir Kohen Gadol is also on his way to bring the Korban Pesach or to his son's B'ris Milah, he must still bury the Meis Mitzvah.
This is not quite the way the Gemara explains it, but principally, I think that it is what you are looking for.
be'Virchas Kol Tuv