You're supposed to turn the engine off immediately when you see the oil light. Serious damage can occur within a few seconds.
Normally the place to start is by checking the actual oil pressure with a mechanical gauge. If it is acceptable, the sending unit is suspect. They commonly leak too but the oil usually drips onto the ground and you don't smell it. If the leak is bad enough to smell, there's a good chance at some point the level got low enough for the oil pump to suck up air. That will cause low oil pressure that can lead to engine bearing failure. Chrysler built a lot of really tough reliable engines, but if you have the 2.7L, that isn't one of them. Once the oil light turned on you can expect major engine damage