Accusative case in both instances.
[1] More precisely an adjective which can apply to a place. When applied to Orchomenos in Boiotia, the epithet distinguished it from another Orchomenos in Arkadia. The Minyans (meaning descendants of Minyas) were supposedly autochthonous inhabitants of various parts of Greece. See e.g. Strabo 9.2.40, and generally OCD(4) s.v. Minyans and Minyas.
[2] The epic/Ionic dialect version of the headword; again sometimes (e.g. Pausanias 9.36.7) applied to Minyan Orchomenos. But note also, with this spelling, Pausanias 5.6.2-3 (quoting Homer, Iliad 11.722-3) on the river Minyeios -- later known as the Anigros -- in Triphylia (western Peloponnese, Greece).