Ignore the other answers to you - they're referring to refined products, not crude. Straight from the strategic reserve FAQ, crude oil doesn't really degrade if stored properly: https://www.energy.gov/ceser/spr-faqs#Q14
Note that if it's not stored properly, it can degrade due to water intrusion and oxidation, and it can just evaporate.
Refined oil products (e.g. the stuff you put in your car) go "bad" because they evaporate. In particular, different substances within the fuel evaporate at different rates, so over time the "mix" degrades away from the optimal ratio. If you put old, degraded fuel into your car it can damage the engine.
You can make fuel last longer by storing it in a cool, dark, airtight place, and there are products you can add to make it last longer, but the general rule is that petrol lasts about 3 months and diesel lasts around 6, or at least that's what I've read.
Entropy, sadly, is an immutable and inescapable law of the universe.
Yes, but the time scale varies widely depending on how it's treated. Gas you get at the pump might start degrading as fast as in a few months, as it's meant for immediate consumption and thus treated less to keep costs down. Gas that's treated for long term storage can go for up to a few years, but that adds extra cost. The main sources of degradation are oxidation and contamination, both from air and impurities. If you can, it makes economic sense to rotate the oil like you might rotate a log file so it's always reasonably fresh.