Can the sin of Deuteronomy Chapter 22 verses 23-23 be classified as adultery and if so did the Sanhedrin use stoning as these verses seem to prescribe or did they still use strangulation?

Shalom, Thank you for your question. The laws of who and how the Sanhedrin carries out the death penalty with can be found in the Rambam - Sanhedrin veha`Onashin haMesurin lahem - Chapter 15 (The Chabad.org site has a full English translation of the Ramabam – I have included a copy for you below). You will see from his ruling that the case mentioned in the verses you quote are listed under the category of stoning (number "d" on the list in halacha 10), whereas the case of adultery is under the category of strangulation (number "a" on the list in halacha 13). As I wrote to you previously, these punishments cannot be applied today – and even in the time of a Sanhedrin, they were used (if at all) very rarely. Halacha 10 The Torah mentions18 people who are executed by stoning. They are: a) a person who engages in relations with his mother, b) with his father's wife, c) his daughter-in-law, d) a maiden who was consecrated, e) a man involved in homosexual relations, f) a man who sodomizes an animal, g) a woman who has relations with an animal, h) a blasphemer, i) an idolater, j) a person who gives his descendants to Molech, k) a person who divines with an ov, l) a person who divines with an yidoni, m) a person who entices others to worship idols, n) the people who lead a city to idol worship, o) a sorcerer, p) a person who desecrates the Sabbath, q) a person who curses his father or his mother, and r) a wayward and rebellious son. Halacha 11 There are 10 people who are executing by burning: a) a priest's daughter who commits adultery, b) a person who has relations with his daughter, c) with his daughter's daughter, d) with his son's daughter, e) with his wife's daughter, f) with the daughter of his wife's daughter, g) with the daughter of his wife's son, h) with his mother-in-law, i) with the mother of his mother-in-law, and j) with the mother of his father-in-law. The latter prohibitions apply if the man has relations with them during his wife's lifetime. After his wife's death, these relations are punishable by kerait alone like other incestuous relationships. Halacha 12 There are two who are decapitated: a murderer, and the inhabitants of a city enticed to idolatry. Halacha 13 There are six who are executed by strangulation: a) an adulterer, b) a person who wounds his father or mother, c) a person who kidnaps a fellow Jew, d) a rebellious elder, e) an a false prophet, and f) a person who prophecies in the name of a false deity. Thus the court executes individuals for a totality of 36 prohibitions. I hope this will be of a help to you – Blessings.