Starts but won't stay started

Hi, I have a 1989 Oldsomobile Ninety-eight. A couple weeks ago I drove it around town, running various errands, and it ran fine - no indication of problems. Then, just the other day, I had trouble starting it. After a few tries, it started, but then backfired and died immediately. I noticed an unfamiliar odor that seemed to be coming from the exhaust. My first thoughts were, “Somebody has put something in my gas tank, because the last time I drove it, it was fine.” This issue was totally unexpected. All the same, I drove it to the grocery store anyway. As long as I kept giving it gas, it would go, but it died at every stop. In order to take off from a stop, I would have to slam it into gear. It ran fine once I got going. Any ideas as to what could be causing this?