Q: Car self-accelerates intermittently

I purchased a used car and three different times (in one month) my car has self-accelerated. After it did this each time, there was a faint oil smell. The car had been sitting for 1 ½ years and before I purchased it, a full tune-up was performed. An oil change was also done and the following were replaced: air filter, muffler bracket, and front brake pads. Two weeks after purchasing it (used), problems began. Slowing down with my brakes while I was pressing on the brake pedal, the car just kept moving; so I slightly slammed on the brake pedal. Immediately following this, there was a faint smell of oil. Two weeks later, this same thing happened. Then today, my car self-accelerated while leaving a parking lot. This time, I did not use the brakes before the self-acceleration. Now… my brakes are squeaking. When the self-acceleration happens, it is always when below 10 mph. The brake light, ETS, oil check light, and check engine lights do not come on. No lights have ever come on. What do you think is causing the self-acceleration and what will solve it?