Well, I don't know what you want to happen in those cases. But you can either create a trigger for each event, or combine several events into one trigger, e.g.
CREATE TRIGGER trig
OR UPDATE OF admin
FOR EACH ROW
Within the trigger, you can have different logic for inserts, updates and deletes if required like this:
IF INSERTING THEN
ELSIF UPDATING OR DELETING THEN
And within the trigger you can look at the "before" and "after" values of the triggering row using :OLD and :NEW, like:
IF :OLD.admin != :NEW.admin THEN
(beware of NULLs - :OLD values are all NULL for inserts, and :NEW values are all NULL for deletes).
As for what the logic of YOUR trigger should look like, I could not possibly know that! I suggest you have a go at it yourself, using the above as a guide, and then come back here if you hit any specific problems.