He wrote variations of popular Scottish folktunes, arranged these for the fiddle and composed other original tunes in the same genre. He published much of his work under the nom de plume "David Rizzio". A "Collection of Minuets " was published in Edinburgh in 1736 and a "Curious Collection of Scots Tunes " in 1740.
In 1741 he left Edinburgh for London and Allan Ramsay lamented this fact in "An Epistle to James Oswald". In London he eventually set up his own publishing house and published "The Caledonian Pocket Companion", a collection of Scottish folktunes, some with his own variations. This ran to 15 volumes and many editions.
He was appointed chamber composer to George III in 1761. Since many of his compositions were written anonymously, research still needs to be done to identify them. He composed in both Scottish and classical 'style gallant' forms.
Contained within the Wighton Collection in Dundee is an MS for "Air for Autumn" in the composer's own hand.
Modern editions of Oswald's Eighteen Divertimento's for two Guitars or two Mandelins and Twelve Divertimentis for the Guittar can be found at the Mandotopia website.