It's that irrawaddyng I've stoke in my aars

Wadding: A soft layer of fibrous cotton or wool used for padding or stuffing. A plug.

"irrawaddyng" therefore is ear wadding, or an ear-plug. Ear plugs are often used whilst sleeping to block out noise. 'Earwicker' is also suggested.

This sounds like Earwicker saying: "it's that ear-plug i've stuck (stoked) up my ears / arse".