Note: See Rav Sternbach below:
There is no obligation to declare the Zero'a, Lechayayim, and Keivah as sanctified, or to separate them from the animal, if they are not going to be given to a Kohen.
This implies that if one cannot get the portions to a kohen before it spoils, then one need not separate them to begin with. If Shem was the Kohen, then Avraham could not have gotten it to him and was patur from separating it.
The gemarah Megilla daf 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)
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.
UPDATE While this does not necessarily apply to Avraham it explains why we are allowed to eat tongue today.
INSIGHTS INTO THE DAILY DAF - Chulin 130
The Tur and Shulchan Aruch also cite the opinion of RASHI (Chulin
136b, DH b'Reishis ha'Gez; Shabbos 10b, DH Haveh) who says that
Zero'a, Lechayayim, and Keivah are not given in Chutz la'Aretz. Rav
Ila'i (Chulin 136b) rules that Reishis ha'Gez and Zero'a, Lechayayim,
and Keivah do not apply in Chutz la'Aretz. In the time of Rav Nachman,
people started to conduct themselves in accordance with Rav Ila'i with
regard to Reishis ha'Gez and no one protested. Similarly, Rashi says,
we do not protest when people conduct themselves like Rav Ila'i with
regard to Zero'a, Lechayayim, and Keivah.
HALACHAH: The Shulchan Aruch
(YD 61:21) rules in accordance with the opinion of Rashi.
QUESTION: The Mishnah states that the laws of Zero'a, Lechayayim, and Keivah apply both in Eretz Yisrael and in Chutz la'Aretz. While
there are various opinions about the obligation to give these Matnos
Kehunah in Chutz la'Aretz (see previous Insight), it is clear that in
Eretz Yisrael even today these Matnos Kehunah must be given to a
Kohen. However, today almost no slaughterhouse in Eretz Yisrael sets
aside these Matnos Kehunah for a Kohen. What is the basis for this
(a) It is the common practice to sell female cattle in whole or in
part to a Nochri, thereby exempting their firstborn calves from the
law of Bechor (see Insights to Bechoros 3:1). Partial Nochri ownership
of the female cattle also exempts these animals from the obligation of
Zero'a, Lechayayim, and Keivah.
However, male animals are not sold to Nochrim, and the Halachah
prohibits selling them solely for the purpose of exempting the animals
from Zero'a, Lechayayim, and Keivah. (This practice was permitted only
with regard to the laws of Bechor, because an animal that has Kedushas
Bechor is subject to many difficult restrictions that must be
(b) One may suggested that no Kohen today is "Muchzak" (proven) to be
a genuine Kohen with regard to the rights to collect Matnos Kehunah.
Since no Kohen can prove that the Zero'a, Lechayayim, and Keivah
belong to him, the owner of the animal may keep them ("ha'Motzi
me'Chaveiro Alav ha'Re'ayah"). However, if this logic is correct, then
it also should apply to exempt a father from performing the Mitzvah of
Pidyon ha'Ben. Since no Kohen can prove that he is genuinely entitled
to the five silver Shekalim of Pidyon ha'Ben, the father should be
able to keep the money for himself. Apparently, the Kohen's Chazakah
that he is a Kohen is reliable enough to obligate the father to give
him the five Shekalim. Why, then, should one not be obligated to give
the Zero'a, Lechayayim, and Keivah to a Kohen?
(c) RAV MOSHE STERNBUCH shlit'a explains that there is a basic
difference between Pidyon ha'Ben and all other Matnos Kehunah. The
obligation to redeem a firstborn son is independent of the five-Shekel
payment to the Kohen. Even when the five Shekalim are not given to a
Kohen, it is necessary to "remove the Kedushah" from a Bechor by
separating five Shekalim as a Pidyon. Since it is necessary to
separate five Shekalim regardless of whether it will be given to a
Kohen, the father must give them to a Kohen even though the Kohen is
not fully "Muchzak." In contrast, Zero'a, Lechayayim, and Keivah (and
Reishis ha'Gez) involve nothing more than a monetary obligation to the
Kohen. There is no obligation to declare the Zero'a, Lechayayim, and
Keivah as sanctified, or to separate them from the animal, if they are
not going to be given to a Kohen. Since one does not need to give them
to a Kohen who is not "Muchzak," one also does not need to separate
them from the animal.