In Aya's case, it is presumably the sound of the husky caw of a crow. The catchphrase was inspired by her opening line in Mountain of Faith. The original line from the game has exactly four 'yas (あやややや〜). In fanart, the number of trailing 'yas vary, depending on Aya's emotional state.
In Karen's case, the catchphrase is the nickname she gives to Komichi Aya.
