The price of the oil is based on what someone is willing to pay for it (QED.)
Right now, nobody wants to buy the oil to actually use it.
So the only buyers are people who are willing to store it now, in order to sell it later when the price is better.
Those people are "pricing in" their costs to store the oil in what they're willing to pay for it on the spot market.
As storage becomes more expensive to procure (demand for it is rising, all the "cheap hotels" are sold out, etc.), the price for oil goes down further to cover those costs of storage for it.
Ultimately, the negative prices are a reflection that nobody wants that oil now, and the more negative, the more a reflection that nobody is going to want that oil for awhile.
So the price of oil at the moment is a function of time (how long no one will want the oil) and the available supply (and therefore price) of storage for the period of time when no one wants the oil.