Farmerman - this exact same thing happened to us -only worse- because we didn't even have an oil tank. We'd bought our house from the people who owned the gas company in town and they'd converted the heat in the house (it was a hundred year old New England farmhouse) from oil to gas - removed the tank in the basement and capped the outside fill pipes.
Well, we lived there for 9 year - redid the whole thing - I mean rebuilt the chimney stripped the woodwork down to the original wood - built a side porch - I'd landscaped the whole thing - it was my dream house.
I came home from work one night and walked in the kitchen and smelt this horrible smell. I called the furnace guy who was a friend of mine - he came over and went down into the basement and said, 'Rebecca - someone's dumped a load of oil in your cellar' - and I mean he was wading through oil up to his ankles - the oil company had been supposed to deliver 500 gallons next door - and the guy came to our house - used a tool to pry off the cap to the pipe and pumped 500 gallons of oil into our basement.
We never spent another night in the house. I have chemical allergies - I can't wear perfumes, I can't go in tire stores or those cheap shoe stores without getting a headache and my son has eczema and asthma. We were both in agony after a half an hour -our lips were swelling and tingling...our eyes were tearing- it was unbearable.
And sad - because I loved that house - but I couldn't risk my childrens' health so we moved into a rented house and the oil company who made and admitted the mistake bought the house at market value and sold it.
The sale process took about six months - and despite their incredibly complicated industrial clean up and their installation of these huge fans to try to air the place out - it never really got better. I'd visit the house and walk in hoping against hope that something had worked so that we could move back in, but the scent was in the carpets - it had saturated our furniture -mattresses-etc. And everytime I spent twenty minutes in the house - I got a headache - my eyes started tearing again...etc.
If you or your children don't have allergies - maybe it'll be okay- because it sounds like a much smaller spill than happened at our house - but I wouldn't know how to tell you to try to get the smell out because we were told that there really wasn't an efficient way - except time...too bad it's winter and you can't really leave the windows open to air it all out.