What are the issues with using sour smelling paint?
The foul smell is from the volatile organic compounds in the paint decaying. Could very well have mold spores living in it. Whatever you are smelling its going straight into your lungs because smells are particular. If it was me I would get rid of it like it was a plague.
My suggestion is get a heavy duty respirator with the proper filters and a boat load of lacquer thinner. Scrub the walls down with the thinner using towels to get as much of that bad paint off as possible. Then apply two coats of Behr Primer &amp; Sealer to the walls. Finally finish by applying a good brand of paint. Lacquer thinner is hard core so:   


cover everything; it will take just about any finish off.
have all your fans running in that room with all the windows open and the door closed.
remove all pets from the home prior to and for several days after the lacquer operation has been completed.
let the walls thoroughly dry out with fans running before attempting to paint.