Cottage living offers something similar to odd jobs. If you talk to the special characters of the world and offer to help with village errands. You can talk to the owner of the market stall, the owner of the bar or the creature keeper. You earn a bit of money and some objects.
Horse ranch also comes with some form of odd jobs.
Sims who work from home and earn money by crafting objects can sell them on plopsy (nifty knitting SP required) to get a higher selling price
If your sim is earning money through any means that is not an official job, they can use the phone and call the ministry of labour to register as self employed. You can give them a job title. If other sims ask for their job in a conversation, they should give this custom job description. I have used this for my archaeologist who earned money with the archeology table.