a. ὀμνύναι τοὺς θεούς may be an abbreviation of ὀμνύναι ὅρκον (internal object) τῶν θεῶν.
b. The accusative is used in asseverations with the adverbs of swearing μά, οὐ μά, ναὶ μά, νή.
Nay, by Zeus: μὰ (τὸν) Δία, οὐ μὰ (τὸν) Δία.
Yea, by Zeus: ναὶ μὰ (τὸν) Δία, νὴ (τὸν) Δία.
μά is negative, except when preceded by ναί. μά may stand alone when a negative precedes (often in a question) or when a negative follows in the next clause: μὰ τὸν Ἀπόλλω, οὔκ
c. The name of the deity may be omitted in Attic under the influence of sudden scrupulousness: μὰ τὸν—ου' σύ γε
Herbert Weir Smyth [n.d.], A Greek Grammar for Colleges; Machine readable text [info] [word count] [Smyth].