how do i remove the oder from a fuel oil spill on my terra cotta floor and bare cement floor and foundation ?

The vapour is not only unpleasant but unhealthy. Assuming that the spillage was by a delivery company [you are hardly likely to pour that amount over it yourself] then they are resonsable for this and should have insurance cover. The concrete is sufficiently porous to absorb the oil. We have friends where a delivery driver let a tank overflow on delivery for a while. More fuel oil than yours, but they are still living with the remnants of the problem and the smell 6 months later. The company is liable for compensation.

Unless this was your fault, let them sort it out. If it is your fault, you would still benefit from professional advice. I have only responded due to our friends experience. This is not the sort of thing that academic chemists normal have experience of! I can only advise cleaning as best as you can, letting it totally dry, then try sealing it with the sort of sealant paint used on garage floors [and sort aircraft hangars]

Additional comment added later: Please do not use volatile solvents in an enclosed basement as suggested by another post. There is a real risk of fire and/or explosion. I'm afraid the charcoal filter in the concrete won't do much good either as the concrete will pretty well seal the charcoal making it rather ineffective. Thorough cleaning using proper emulsifying agents [detergents] 2-3 times is the key, then washing that away and allowing to dry properly before sealing

Fuel Oil Spill In Basement

Not easy! ...DON''T PAINT OVER IT ....First with rags rub and rub and rub up all you can, .... then use new rags with a solvent ,alcohol first choice, or acetone, petrol last but cheapest choice plenty of ventilation (no smoking) the solvent smell will not linger too long. This is a very challenging problem don't expect to remove all the oder. Continuous ventilation is the key . Painting is a very bad idea ,it will not adhere to an even slightly oily surface, and will not prevent the oder . Try sprinkling charcoal around the floor it absorbs all oders Last resort would be to lay a few inches of concrete with a few % crushed charcoal mixed in. Good luck!