My car starts but won't stay started once I stop turning the key.

My car has been sputtering/chugging when idling since I purchased it. I was told to replace the air filter and have done so. I was driving on the highway yesterday and it started chugging/sputtering again. I pulled over and the car sputtered and died. It starts but won't stay started. The engine light came on before I pulled over and has since shut off. The oil light is on every time I've tried to start the vehicle. (normally it shuts off after awhile) Do you know what is wrong other than just the car being ancient?