Let's start with the 7 numbered clues. These represent the following:
1. An Australian singer-songwriter = SIA
2. The second part of a certain country's name = RICA (Costa Rica)
3. A plant genus = ERICA
4. A plant genus = ERICA (again)
5. The International Cat Association = TICA (its acronym)
6. A 1948 movie directed by _________ = (to be solved shortly...)
7. A variant of Leah or Lea = LIA
What are these? They are the:
endings of the names of continents:
ASIA, AFRICA, NORTH AMERICA, SOUTH AMERICA, ANTARCTICA, ..., AUSTRALIA (in place of 'Oceania').
This means clue 6 must in some way indicate the missing one, and this can be done if it reads:
6. A 1948 movie directed by ALFRED HITCHCOCK = ROPE
...since this is the tail end of the missing continent, EUROPE.
Returning to our 5 sets, what are these? Substitute what the 7 answers represent into their sets to get...
...groups of continents. And how are they grouped? In terms of the oceans that they border:
A = {ASIA, NORTH AMERICA, SOUTH AMERICA, AUSTRALIA} = PACIFIC
B = {AFRICA, NORTH AMERICA, SOUTH AMERICA, EUROPE} = ATLANTIC
C = {ASIA, AFRICA, AUSTRALIA} = INDIAN
D = {ANTARCTICA} = SOUTHERN
E = {ASIA, NORTH AMERICA, EUROPE} = ARCTIC
As confirmation, notice that the two lists are complete and ranked in order.
i.e. There are precisely 7 continents and 5 oceans on Earth, and both the continents and oceans are listed in order of decreasing size.
One final note:
In my original solution I had 'South AFRICA' as a legitimate solution to #2; however, as @Marius points out in comments, 'Costa RICA' also works here, and is much more satisfying since it does not give the entire name of the continent all at once.
