Crude oil and it's vapors are highly toxic. Maybe you could store it there if you capped the giant hole, but that wouldnt be feasible.

https://www.amfs.com/effects-of-crude-oil-exposure/

Why wouldn't you have leeching problems? If you filled that mine up the oil at the bottom would be under a lot of pressure.

This is no different than when it's in the ground naturally.

Those pits fill up with water once they're decommissioned unless you're in a dry region. The rocks usually have fractures which allow surrounding ground water to leak into the pit, only reason they don't flood is because you lower the water table around the pit in the years before.