I'm not so sure about your initial premise, that this sharp drop in oil prices has had an independent effect on the stock market. I don't really follow what the major indexes are doing (like the Dow, S&P 500, etc.) but the big pharmaceutical stocks I do follow have been doing pretty well, and I don't think stocks have gotten hit anywhere near as hard as oil has.
Oil is down 80% this year. In comparison, the S&P 500 is down 15-16% from its ATH.
What worries me is the oil market reflects actual global economic activity. If oil demand is this low, it suggests the global economy is really crashing. The stock market meanwhile is completely speculative, running off optimism that an imminent economic reopening will reverse all the economic damage from the past 2 months, and life will just go back to normal.
I think stock investors have their head in the clouds. Businesses can't just shut down for months and reopen as if nothing happened. The bailout loans are going to leave many companies up to their eyeballs in debt. Consumers are also losing confidence and are making much less money now. I don't expect job numbers to return to January 2020 levels for a long time. A lot of these "temporary" furloughs will become permanent job losses when businesses realize economic demand has plummeted.
Do I think stocks will keep grinding upwards for a while longer? Yes, but I also think this relief rally will end in tears.