JKR said that James supported Lupin after they left school. Sirius could support himself because of the gold his Uncle Alphard left him. I guess that would mean paying the rent and bills etc on a small flat or something while they were in the Order. I guess that he'd only have gone into a full time job after Voldemort fell and the Potters were killed. Perhaps the fact that he'd been in the Order made it easier than it might have been to get a job, or maybe Dumbledore recommended him for something.
Personally, I don't think he stayed in one job for long, rather he moved from job to job when either people found out about him, or he was sacked. He's very good with Dark creatures and remedies, so I would have though he'd had jobs in those areas. Perhaps he went abroad where they might be more tolerant, or just ask less questions. I think that the type of jobs he had weren't very well paid considering the state of his robes etc.