One of the great things about the Roman Catholic Church is that they document everything, including decisions made 1,600 years ago. So we actually do know what happened to each book.
The early Christian Church used the Septuagint as the principle work to use because it was considered to be based off of older Hebrew texts, and thus more accurate to the original Hebrew. However, over time that view fell out of favor from both Jews and the Church.
When St. Jerome first compiled the Vulgate in the 5th century, he compared the Septuagint to other Hebrew translations and found the Hebrew translations to be more accurate. As far as I understand, in the intervening years, the Jews came to the same conclusion independently.
So when the first Vulgate in 405 was compiled, decisions were made as to what was accurate and what wasn't. Works that had some basis in the Hebrew translations available at the time were kept, and others that were called into doubt were dropped.
In this respect, it's no different than the Protestant omissions a thousand years later: when new information comes to light that substantively challenges the authenticity of the work, they're removed.
However, the Eastern Orthodox Churchs continue to rely on the Septuagint as the main translation, in contrast with Jerome and the editions that came thereafter in the Roman Catholic and Protestant faiths.
To the specific works:
1 and 2 Esdras
These two are easy. The Roman Catholic Church calls these books Ezra and Nehemiah and they are part of canon, appearing after 2 Chronicles and before Tobit. As far as I understand, the principle differences between the two are that 1 and 2 Esdras contain a fair amount of restructuring and reordering from the original work (the Jewish single volume Ezra) and are from the Septuagint, whereas Ezra and Nehemiah are from the Hebrew tranlsation.
3 and 4 Maccabees
These were never considered to have any claim to canonicity, and have never appeared in any Roman Catholic canon. The Catholic Encyclopedia has this to say:
III Mach. is the story of a persecution of the Jews in Egypt under Ptolemy IV Philopator (222-205 B. C.), and therefore has no right to its title. Though the work contains much that is historical, the story is a fiction. IV Mach. is a Jewish-Stoic philosophical treatise on the supremacy of pious reason, that is religious principles, over the passions. The martyrdom of Eleazar and of the seven brothers (2 Maccabees 6:18-7) is introduced to illustrate the author's thesis. Neither book has any claim to canonicity, though the first for a while received favourable consideration in some Churches.
Psalm 151 isn't part for the Roman Catholic (or Protestant or Jewish) canon because most scholars of those faiths believe it to have been written after the rest of the Psalter, making it not part of the original work. It didn't make it into the original Vulgate.
Prayer of Manasseh
For the Prayer of Manasseh, it was relegated to the Appendix of the Roman Catholic Bible (until recently, the Clementine Vulgate) in 1592 by Pope Clement VIII after appearing in the original Vulgate. Originally, it appeared at the end of 2 Chronicles.
However, at the time, most people, Protestant and Roman Catholic alike, viewed the Prayer as apocryphal, namely because there were no reliable Greek or Hebrew translations (a fact overlooked in 405, where an Old Latin translation was added). However, because it's appeared in the Bible for so long, it was relegated to the appendix as a means to preserve it without having it disappear entirely.