I have heard and read the oughties for 2000-2009.
This seems to me strange, as I have never heard anyone say, for example, 'twenty ought five'. My grandfather did speak of '(nineteen) ought five', but he was one of the last people I knew to use the word 'ought' in this way. Not all dictionaries record it. Of those that do, most seem to prefer the spelling 'aught'. Several label it 'older/less common form of nought' or even 'archaic'.
See more here."Annual income twenty pounds, annual expenditure nineteen pounds nineteen and six, result happiness. Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery."