I believe the last two themes were the Elves and the Men
Tolkien discusses The Music of the Ainur in Letter 212.
He begins by describing what you refer to as the first theme the Design propounded to them by the One.
The Ainur took part in the making of the world as 'sub-creators': in various degrees,
after this fashion. They interpreted according to their powers, and completed in detail, the Design propounded to them by the One. This was propounded first in musical or abstract form, and then in an 'historical vision'. In the first interpretation, the vast Music of the Ainur. This was propounded first in musical or abstract form, and then in an 'historical vision'.
The Letters of JRR Tolkien: Letter 212
Ho goes on to refer to what you call the second theme as alterations made by Melkor.
In the first interpretation, the vast Music of the Ainur, Melkor introduced alterations, not interpretations of the mind of the One, and great discord arose.
After describing how the One made the 'historical vision' a reality ("Eä") and how many of the Ainur chose to enter into Eä, Tolkien goes on to discuss Elves and Men.
Elves and Men were called the 'children of God', because they were, so to speak, a private addition to the Design, by the Creator, and one in which the Valar had no part. (Their 'themes' were introduced into the Music by the One, when the discords of Melkor arose.) The Valar knew that they would appear, and the great ones knew when and how (though not precisely), but they knew little of their nature, and their foresight, derived from their pre-knowledge of the Design, was imperfect or failed in the matter of the deeds of the Children.
Note how the letter say that their themes (plural) were added by the Creator. I take it from this that what you refer to as the third and fourth themes are the two themes that represent Elves and Men.
Tolkien also referred to the themes (not theme) of Elves and Men in Letter 257.
In O[xford], I wrote a cosmogonical myth, 'The Music of the Amur', defining the relation of The One, the transcendental Creator, to the Valar, the 'Powers', the angelical First-created, and their part in ordering and carrying out the Primeval Design. It was also told how it came about that Eru, the One, made an addition to the Design: introducing the themes of the Eruhîn, the Children of God, The Firstborn (Elves) and the Successors (Men), whom the Valar were forbidden to try and dominate by fear or force.
The Letters of JRR Tolkien: Letter 257
I believe that in the Letter, Tolkien describes the Music as consisting of:
- The Design created by the One.
- Alterations to the Design added by Melkor.
- The theme of the Elves, created by the One.
- The theme of Men, created by the One.
Different versions of the mythology
Tolkien worked on the mythology over a period of decades and produced many drafts that differed in both major and minor details.
I believe Mark Olson's excellent answer is based on what Christopher Tolkien refers to as "Version C" of the Ainulindalë, which is printed in Morgoth's Ring (Volume X of The History of Middle-earth). I believe that version was completed by the early 1950s.
My answer is based on letters written by Tolkien in 1956 (Letter 212) and 1964 (Letter 257). I don't point this out to try to argue that the version in Letters is later and so must be "correct", I'm simply explaining why there can be two incompatible answers that both quote Tolkien's writing.
As to which version is correct, Tolkien didn't get around to publishing either version, so we can't know which he would have picked (or he might have written a third version). We are all free to pick the version we prefer.