Oil leaked after service

I'm assuming that there was no leak before the oil and filter change, and that the leak was caused directly by the oil and filter change.

Most likely the oil filter has been dramatically overtightened, causing the rubber seal on it to split, allowing oil to leak out of it.

From where I am, it's impossible to tell if your engine is damaged. I would immediately stop driving the car, and change the oil filter. Ensure its not over-tightened (0.5 - 1 turns after its snug is enough), and refill the engine oil.

It depends when the oil started leaking.If the oil leaked only while the car was parked then there is no need to worry.However if you have driven the car while the oil was leaking chances are you would have damaged your engine. As you have mentioned warning lights did not come on the dash there is a fair possibility the oil leaked while the car was parked. If you have not driven it on a very busy road you can back trace a few miles to see if there is oil spillage on the road. Also you can call the service centre to visit your place to have it inspected and top up the oil.

The engine probably has some internal damage, but its probably going to be okay if it hasn't seized completely already. The only thing you can do is have it towed to a shop, have them do an oil change, check for leaks, and keep going. Have them check to see if you blew up the engine first though.