In a large frying pan over medium heat, cook the sausages, breaking up the clumps with a wooden spoon and stirring occasionally, until lightly browned, about 10 minutes. Transfer to a large bowl and discard the fat in the pan.
Return the pan to low heat and add the oil. Add the onions and celery and cook, stirring occasionally, until soft, 7–8 minutes. Add to the bowl with the sausage.