What plumbing issue would make a smell like old fry oil or parmesan come from basement if water runs upstairs?

The house was inspected by a plumber when bought so this is something a plumber could have missed on a routine inspection. Although it is not the only smell, it is the strongest: it comes right up through the vents, and even from outside around the basement and is like FOOD- like old fry oil, or parmesan cheese or rotting vegetables. It gets so bad in the basement when someone is using the water up here in the bathroom, like a long shower, flushing the toilet, etc., that it actually wafts up through the vents. It seems worse on warm days and in the morning. It is not as bad on rainy days. If it helps or could be connected, there seem to be three distinct smells; in addition to the main plumbing issue that causes this odd food smell, there is also a sewer gas odor (like the smell coming up from the pipes in a poorly maintained old public bathroom) that *possibly* is lessening slowly since I had my boyfriend prime the traps but still seems to be there some; and like in most old houses there is a bit of a musty damp basement smell that is really not that bad at all and we just bought a dehumidifier for that. The combination of all three odors in the basement is so bad now that because the central air pulls the air from the basement, I no longer use it. I asked if we can call a plumber but my bf wants to call the same plumber that missed this in the first place. So, what in plumbing in an old country house could make it smell like I live above a nasty greasy-spoon diner every time someone takes a shower or flushes?