What Torah Laws Did Avraham Observe

"Avraham listened to My voice,  observed My safeguards, My commandments, My statutes and My teachings" (Bereishit 26:5)

If we follow the approach of interpreting these nuances as the plain text, we must assume that G-d spoke of the Seven Noachide Laws which are applicable to all of mankind.  The word mitzvotai then applies to the prohibition of robbery and bloodshed; the word chukotai applies to the law not to eat tissue or blood from a living creature, as well as not to mate different species of animals with one another or to do the same with trees by crossbreeding.  The word torotai refers to the prohibition of all kinds of idolatry as well as to the positive mitzvah to establish a judiciary.  People observing these laws are considered to be doing G-d's Will.  Finally, vayishmor mishmarti (keeping G-d's safeguards) is a reference to "fences" around Biblical mitzvot to ensure that even if a "fence" had been violated, the Biblical mitzvah itself would remain inviolate.

According to Bereishit Rabbah 64:4 Avraham was familiar even with such concepts as making an eruv in private property to avoid becoming guilty of transferring property from one domain to another on the Shabbat.

There is a view expressed in the same Midrash that the tractate Avodah Zarah dealing with idolatry and its sub-categories studied by Avraham was comprised of 400 chapters.  The repetition of the word mishmarti after G-d had already said that Avraham observed, i.e. vayishmor, is a reference to secondary incestuous relationships which were not even spelled out in the legislation concerning forbidden (sexual) marital relationships in the Written Torah.

The opinion of our Sages is that the words vayishmor mishmarti refers to Avraham observing voluntarily all the laws of the Torah which had not yet been legislated. (Rabbeinu Bachya)