Maybe try a de-humidifier... I have one in the house to get rid of the musty wet smell. It's a very old house, and one of the storage rooms had too much moisture and dust circulating in it. It works very well.
Your apartment just probably needs better ventilation, or there's a leak somewhere. I would have an inspector check it out if you're unsure where to start.
Too many indoor cats in a household would be good enuff to cause a sour smell. No mater how many times a day you get the cat cookies out of the litter box, the place ll smell sour as tha cats will be marking the whole place up over and over with layers and layers of their piss.