Sir Henry Yule and Arthur C. Burnell explained in their Anglo-Indian dictionary, Hobson-Jobson, published in 1886, that the word was used in the names of several kinds of exotic foreign things, especially those that the British had brought into the country, such as the aubergine, विलायती बैंगन (vilāyatī baingan), and especially to soda-water, which was commonly called विलायती पानी (vilāyatī pānī, “foreign water”).
Blighty was the inevitable British soldier’s corruption of it. But it only came into common use as a term for Britain at the beginning of the First World War in France about 1915. It turns up in popular songs "There’s a ship that’s bound for Blighty", "We wish we were in Blighty", and "Take me back to dear old Blighty, put me on the train for London town", and in Wilfred Owen's poems, as well as many other places.
The sense of a minor wound comes from attributive use of the noun, as in “a Blighty wound,” “a Blighty one,” 1916.
In modern Australian usage, Old has been added, as in Old Country and Old Dart, as a sentimental reference to Britain.