Why did Lavan add "Elohei Avihem", and why did Yakov swear by Pachad Yitzchak?
Seforno: He was explaining that he appointed the god of Nachor together with the G-d of Avraham, because he was also the god of Terach, who was the father of them both. However, Yakov swore by the G-d whom his father Yitzchak feared, 1 for Yitzchak was not the son of Terach.
Tosfos ha'Shalem (4): Yakov swore in the life of his father Yitzchak, who did not normally swear, so this was a great matter. 2
Ramban: Pachad Yitzchak is Hashem's Midas ha'Din.
Oznayim la'Torah: Lavan referred to 'Elokei Avraham' - whose Midah was Chesed 3 and who entered into a (positive) covenant with Avimelech and swore to him that they would do good to each other. But that was not the gist of the covenant here, 4 which entailed not doing har to one another, 5 which was similar to the covenant that Yitzchak entered into with Avimelech. 6 Which explains why he swore by 'the G-d of Pachad Yitzchak his father'
Why did Yakov swear and not Lavan?
How could Yakov accept an oath in the name of idolatry? "Lo Yishama Al Picha" (Shmos 23:13) forbids this!
Moshav Zekenim: Perhaps Yakov knew that [Nachor] did not serve idols (so Elokei Nachor is Hashem). 1
Refer to 31:53:2:1.
If so, when a scribe writes Elokei Nachor, he must intend that it is Kodesh! Lavan said also Elokei Avihem. Terach was an idolater! However, he repented (refer to 15:15:2:1); perhaps 'Elokei Avihem' is Kodesh, based on his final belief. Maseches Sofrim (4:7) and Maseches Sefer Torah (4:4) say that both of them are Chol. Bereishis Rabah (74:16) and other Midrashim say that Elokei Nachor is Chol, and Elokei Avihem is Kodesh (Matanos Kehunah - due to Terach; Etz Yosef - for it includes Avraham), and Chol (PF).