The gemarah Megilla dafr 28a brings the case of Rav Preidah who said that as a middus chassidus he had never eaten from an animal from which the matanos had not been taken. The Art Scroll edition of the gemora on daf 28a (1) footnote 4 brings the Ritva who says that
The Gemora concludes that there is no analogy between the meat of an animal whos gifts have not been separated and tevel. ... Also in contrast to terumah, the priestly gifts from an animal are non-sacred, and so may be eaten even by a non-Kohen. Nevertheless, Rav Preida went beyond the demands of halacha, refusing to eat meat from an animal whose priestly gifts had not been separated (Ritva)
Since Avraham kept the Torah as a midus chassidus and on that basis is halachically allowed to eat tongue as well as serve it to his guests.
On thinking it over further, I have come to the conclusion (through logic) that Avraham would have also been considered a kohen at that time (when the "guests" arrived). He had taken on the spreading the worship of Hashem and was busy doing the avodah (of that time). In fact, that is why we have the line of kehunah being thought of as Shem (who outlived Avraham), Aiver, Avraham, Yitzchak, Yaakov, Levi (as seen by the treatment of the tribe of Levi in Mitzraim). It was only after Matan Torah that we have the assigned kehunah and the specific matanos.
Since we can treat Avraham as a kohen, he was allowed to assign the matnos kehuna to himself, and, since they were not kodesh, serve them to his guests.