First things first, the oil leak... If it is the rear main seal then turn the radio up 'cause it's gonna cost you a bunch to fix 'cause the engine has to come out...
"Check engine" light??? Could be anything related to the fuel injection, exhaust and/or ignition... A loose/bad spark plug wire, as John says, will make an engine miss when nit is cold or damp... If that is what it is it will improve (smooth out) after the engine warms up... It could also be a crack in the distributor cap allowing moisture inside the cap and like the bad wire or connection may smooth out when the engine is warm... Either way, it's okay to drive... If the engine doesn't die when it is cold then start it and let it warm up for 10 minutes or so...
Since the car passed emission there probably isn't anything wrong on the fuel injection side or the exhaust side... Either will give you bad readings... It doesn't hurt, however, to run a can of fuel injector cleaner thru a full tank of gas now and then...
Here's something you can do, Janie... Wait until after dark and start the engine cold, let run, open the hood and look for small flashes of spark from around the spark plug wires and ends... If you see anything like that then you have found yer problem...