Change Oil Light coming on at odd time

I had the car in at Thanksgiving time. It needed a new battery, second year in a row–beside the point. But it had been smelling hot and smoking like for ever since I could remember even on short drives. The mechanic said oil was all over and had to wash it all inside. It doesn’t use much oil, but I did add some occasionally when I used to drive a lot. In Nov., he changed oil and overfilled about 1/2 qt at least. He thought all ok and no problem–no major leak or anything, but it still smells hot and the oil looks black and I have driven it very little and oil is at fill still as overfilled. I am estimating maybe 500 to 1000 miles driven would be TOPS.
Should it be so black? The CHANGE oil light comes and stays on. I know time wise, it is time to change the oil, but it is hardly driven. Is the light controlled by time and not usage (mileages)? Should I be concerned with the black color and change light since I hardly drove it?
Is it ok to drive a couple hundred till I can get it in to change? I have a trip to take. THANKS.

Your Impala is how old? It must be fairly new to have an “oil change” light, but since you’ve bought several batteries for the car it might be an older Impala and what you call an oil change light might be something else.

Black oil in 500 to 1000 miles seems odd. If this oil change light is really an oil change light and the oil is black you should get it changed. Since you are taking a trip this might be the time to use a quick oil change service and get the oil changed now before your trip.

It seems there are some problems with your car. The motor compartment shouldn’t be dirty with an oily film on everything. Someone needs to find the source of this oil and correct it.

We need to know more details, including:

Make, model, and model year (I assume that the car is an Impala, but…)
Odometer mileage
Engine type/size
How the car is actually driven (Were those 500-1000 miles accumulated in a few long drives, or is the car typically driven locally for just a few miles at a time between stops?)
The car’s maintenance history over the past 3 years

Incidentally, the receipt for that last oil change should have noted the odometer mileage at the time, so a little bit of subtraction should allow you to know exactly how many miles have been put on the car since that November oil change.