I never say 'på sekundet' when I mean immediately. I say 'med en gang'. 'Straks' and 'med det samme' and 'med en gang'. mean the same. If something happens to me and I need my husband's help immediately, I call 'Du må komme med en gang!' (You must come immediately.) I wouldn't use any of the other expressions.
So this literally means "on the second", is that right? The sense is "(do something/something happens) this very instant"?
Exactly! Not to be confused with the English phrase "in a second", which means something different.