Mioko (voiced by Kana Hanazawa) uses some kind of unusual speech pattern which the subtitles translate into vaguely US Southern dialectal English:
Specifically, I can hear her using ora to refer to herself and ending her sentences with de gasu instead of desu. Wikipedia says ora is an informal pronoun with rural connotations, and this Google Books result says de gasu is a contraction of de gozarimasu, a very polite form of de aru.
You can hear it for yourself in Episode 7 starting around 24 seconds in.
Is Mioko's accent a specific regional accent, or is it just one of those made up bizarre speech patterns that anime specializes in?