What is the source for expounding the torah according to remez, derush and sod (along with 'pshat' the group can be referred to by the acronym PaRDeS)?
These forms of hermeneutics are not found in the list of Rabbi Yishmael on the 13 ways to expound the torah, nor do they have a logical basis.
Hacham Ovadia in Yechave Da'at 4:47 quotes Morenu Harav Haim Vital (1543-1620) who speaks about this concept in Sha'ar Hagilgulim (Hakdama 11) and in his introduction to Sha'ar Hamitzvot. He seems to get it from the Zohar Parashat Balak (202a) which says:
והיה כעץ שתול על פלגי מים, מה אילן זה יש בו שרשים ויש בו ענפים ויש בו עלים ויש בו פרחים ויש בו מוח וכו', כך התורה יש בה פשוטי המקראות, דרשות הפסוקים, רמזי החכמה על ידי גימטריאות ונוטריקון, וסודות נעלמים וכו
So, it seems, the oldest and primary source for PaRDe"S explanation is the Zohar.
(Disclaimer: I have not seen/looked into any of the primary sources inside other than the excerpt above. I only quote Hacham Ovadia.)
Scholars have written much about this issue. Here is the summary of A. Van der Heide:
The origin of the acronym Pardes can be established with some precision. Following the initial research carried out by W. Bacher, Gershom Scholem convincingly traced the invention of the highly evocative pun to Moses de Leon... In all probability it was introduced by Moses de Leon in a book called Sefer ha-Pardes, which he mentions in at least two places. The book itself is not extant. The idea found its way to the later parts of the Zoharic corpus, the Ra'ya Mehemna and the Tiqqune Zohar, and from there is spread to other works.
Gershom Scholem in his article “The Meaning of Torah in Jewish Mysticism” in On the Kabbalah and Its Symbolism (New York: Schocken, 1996), 32-86, noted that the development of a fourfold hermeneutical method appeared simultaneously in the works of R. Moshe de Leon, R. Yosef Gikitilla and R. Bachya b. Asher. The description “Pardes” for this fourfold interpretation belongs to R. Moshe de Leon, in a lost work of that name, and became widely known through the Tikkunei Zohar.
See also M. Idel, “Pardes: The Fourfold Method of Interpretation” (Appendix I) in Absorbing Perfections: Kabbalah and Interpretations (New Haven, Conn.: Yale University Press, 2002), pp. 429-37. Idel argues that the tiered “Pardes” hermeneutic allowed Kabbalists to locate kabbalistic interpretation in “a place of honor” without replacing existing methods of exegesis. According to late thirteenth century kabbalists, the “four who entered Pardes” each reached one level of PaRDeS. Likewise, Pardes was seen to correspond to four worlds of ‘atzilut, beriah, yetsirah and ‘asiyah. The kabbalist climbs successively through these worlds by means of the pardes method.
B. Sack, The Kabbalah of R. Moshe Cordovero [Hebrew] (Jerusalem: Bialik Institute, 1995) pp. 113-139, discusses the view of R. Moshe Cordevero, according to which the four levels of souls correspond to the four levels of understanding Torah, PaRDeS, and the four worlds.
The earliest I can find of those four categories being mentioned together is in the writings of Rabbi Moshe Alshich (a kabbalist from Tzefat; 1508 - 1593). He writes in his commentary to Genesis 1:27 as follows:
וכל זה על ידי קיום התורה אשר גם בה ארבע בחינות אלה שקשורים זו עם זו, הפשט כנגד עולם השפל, רמז כנגד השני, דרש כנגד השלישי, סוד כנגד העליון
（I leave this untranslated because I don't really know what it means. CYLK)
Rabbi Chaim Vital, Sha’arei Kedushah 1:2, s.v. u’zkhor v’al tishkach; Sha’ar HaMitzvos, Hakdamah, s.v. gam b’inyan eisek haTorah; R. Yehudah Ftayah, Minchas Yehudah, Yirmiyahu, 86 (p. 131), and Tehillim, 93 (p. 202) -- in addition to the other mekoros cited here.
