Once the oil is finished the lights will go out and life as we have been accustomed to will be gone forever...
The oil is never 'finished'. Production will never cease under Peak Oil theory and it will always be available. What Peak Oil does predict is that demand will eventually outstrip supply because supply falls. The price (in real terms) then rockets up as customers compete for what's available. Many people become priced out of the market and cannot buy fuel or the products its made from. But oil never actually runs out.
How will that affect bitcoin? Well, if the situation ever arises I think we have far more important things to worry about than an internet commodity. Like food, water, and security.
I think we hit peak oil around a decade ago, the price rose above $100 in the few years after and has never really fallen below that for any significant period of time,
despite record prices, oil companies havent bothered to make new refiniries as they take around 30-40 years to ROI(including build time, planning etc) and if they arent building them while making records profits annually then they must know more than what they let on
But the oil will eventually run out as its a finite resource...
