I agree that you likely have a bad case of H. Pylori.
However, that's not the source of the odor. Pylori is aerobic and smells of ammonia. But it also lowers Gastric Acid. In some cases, it lowers Gastric Acid to the point of Achlorhydria. Under such conditions, foul-smelling anaerobic bacteria are able to survive in the stomach and go to work on putrefying food and smelling horrible. And yes, you would expect the odor to vary according to what you ate.
Another thing to be aware of is that Low/No Gastric Acid allows other Pathogenic Microbes in, and allows your normal Flora to overgrow, potentially causing SIBO type symptoms.
If it were me, I would see an MD on this, and mention Pylori, SIBO, and Low Gastric Acid. If you take the Antibiotics , consider taking an antifungal such as Nystatin at the same time to avoid causing a Yeast Overgrowth.
In the meantime, you can get some relief from the odor by supplementing with Betaine HCL and a good digestive enzyme that contains Oxbile. This will help break down undigested food and kill those anaerobic bacteria.
If you want to treat it on your own, it can be done, but will take some time and effort.
Here is a nice blog by a woman who successfully treated her Pylori. Many of the supplements she used also treat SIBO. I differ in opinion on a few points, but overall, I think it's a good read.