"Collectively, all of us humans, all 7 billion of us, breathe in about 6 trillion kg of oxygen every year. But our atmosphere contains a whopping 1 quintillion kg of oxygen." (Vsauce) Mathematically speaking, even with the account of all other life on Earth breathing the same air, it would take thousands of years to run out. This is good news, if you're not a plant. Without the sun most plants would most definitely die off, but surprising enough some large trees, such as oaks and redwoods, have enough sugars stored in them to stay alive for potentially years in the dark. It's not the dark they have to worry about it would be the cold.
The average surface temperature of the Earth, seasons and climates considered, is about 14C (57F). Without the enjoyable warmth of the sun, the Earth would lose heat exponentially at first but slowly decrease as time went on. Within the first week, approximately, the average would be at freezing, 0C (32F). This in a survival standpoint isn't bad so we could get by for the first week or even the first month, but by the end of the first year, post sun, we'd be singing a different tune. By then the average would be -73C (-100F), so the term cold wouldn't even cut it anymore. The most reasonable strategy to beat the cold would be to move to geothermal hot spots, like Yellowstone or Iceland. This is because the Earth produces its own heat. "20% of this warmth came from the fact that when the Earth formed, mass crushed so tightly in the middle, that the pressure liquefied rock. The other 80% of Earth's internal heat comes from the fact that deep in its core, radioactive elements decay; providing the energy needed to keep the Earth's core at 5000C (9000F)" (Vsauce).Despite this, it's still surprising how much we depend on extraterrestrial energy i.e. the sun, this is far from the end for us. And it's now that things get a bit weird and a lot more "science-fictiony.