Rabbi Avahu referring to himself in the 3rd person: Kiddushin 31b
Rabbi Avahu's manner of speaking in clever riddles: Eruvin 53b
Rabbi Avahu's riddle response when the students asked him where Rabbi Ilai was, and Rabbi Ilai's riddle response when the students asked him where Rabbi Avahu was: Eruvin 53b
Rabbi Avahu's second wife (according to one reading) was the daughter of a Kohen: Eruvin 53b
The respect with which his son, Avimi, treated him: Kiddushin 31b
Giving an answer to Rav Tachlifa of Israel via hand-motions: Bava Metzia 7a
Rav Chisda taught a lesson from a verse, which Rav Tachlifa, from Israel, heard and re-told to Rabbi Avahu. Rabbi Avahu provided a different verse for the lesson: Eruvin 54b
Answering a question "Yes" at times and "No" at others, uncertainly: Shabbat 116a
Would sit on a stool on Erev Shabbat building the fire for Shabbat: Shabbat 119a
Would have an entire animal prepared for the Post-Shabbat Meal, from which he would eat only the kidney: Shabbat 119b
Establishing the practice for the blowing of the Horn Blasts in Caesaria on Rosh HaShanah: Rosh HaShanah 34a
Talmud concluding that a statement of his is "a lie [Beduta/Beruta]": Bava Metzia 9a
Rabbi Avahu asking Rabbi Yochanan how to do a certain mitzvah, and Rabbi Yochanan replying with advice based on Rabbi Avahu's general views, even though Rabbi Yochanan personally disagreed: Berachot 24b
Set of Rabbi Avahu's statements relating to rainfall and prayers for rain: Taanit 6b-7a
Rav Yitzchak bar Yosef meeting Rabbi Avahu in a public gathering in Usha: Ketuvot 50a
Rabbi Avahu was so strong that when the bathhouse floor collapsed beneath him, he was able to hold up with one hand the two men who had been supporting him, and to use his free hand to climb a pillar. He only wanted the supporters in order to conserve strength for his old age: Ketuvot 62a