The Dictionaries list this as an Interjection,
stone the crows, (UK, Australia, informal) Generalised expression of surprise or amazement, or just for emphasis.
The exact origins of stone the crows is not so clear. It seems there were a number of similar fragmentary sentences around Australia in the early decades of the twentieth century, all fuelled by the Australians love of playing with language. Reference is made to stone the crows in [Rose of Spadgers by C.J.Denis, 1924] and in the BBC radio comedy [Hancock’s Half Hour, 1950’s].
Taking it a step further and looking at possible meanings for the word crow,