Question: What is the difference bewteen Sifra, Sifre, and Sifrei?
Answer: Sifra ספרא is an halakhic midrash on Leviticus, and is also known as Torah Kohanim or Sifra de-Vei Rav.
Passages from Sifra are usually cited from I. H. Weiss's edition (Vienna, 1862, reprinted in New York, 1947) Reference Oversize BM517.S63 W42 1862a. A partial critical edition was edited by Finkelstein: Sifra on Leviticus, According to Vatican Manuscript Assemani 66 with Variants...Reference to Parallel Passages and Commentaries (New York, 1983-1991) Reference BM517 .S6 1983. Neusner has translated the text into English in Sifra: An Analytical Translation (Atlanta, 1998) Reference BM517.S6 E5 1988
Sifrei and Sifre are alternate transliterations of the Hebrew term ספרי
Sifre Bamidbar and Sifre Devarim are halakhic midrashim on Numbers and Deuteronomy, respectively. Sifre is also known as Sifrei de-Vei Rav. Sifre Zutta is an halakhic midrash on Bamidbar which exists only in fragmentary form.
A critical edition of Sifrei Numbers was edited by H. S. Horovitz: Siphre d'be Rab (Leipzig, 1917; 2nd ed. Jerusalem, 1966). BM517 .S74 1917. English translations are: Midrash Sifre on Numbers...by Levertoff (London, 1926) BM 517 S74 A3 1926 and Sifre to Numbers: An American Translation and Explanation by Jacob Neusner (Atlanta, 1986) BM 517 S74 A3 1986.
The critical edition of Sifre Devarim is: Sifre on Deuteronomy, by Finkelstein (NY, 1969) BM517 .S75 1940a. English translations are: Sifre: A Tannaitic Commentary on the Book of Deuteronomy...translated by Reuven Hammer (New Haven, 1986) BM517 S75 A3 1986 and Sifre to Deuteronomy: An Analytical Translation by Jacob Neusner (Atlanta, 1987) BM517 S75 A3 1987.
A good introduction to these and other midrashim is found in H. L. Strack's Introduction to the Talmud and Midrash, located in the JTS Library at Reference BM 503.5 S7 .