Oil was famously the victim of a bubble that took it to $140. It was separate from the housing bubble, which peaked in late 2005, and the finance bubble, which peaked in late 2007. Oil continued to rise at an increasing rate through both of these, and peaked and crashed right in the middle of 2008. The Internet is awash in graphs of these events.
Oil and food are segregated from the Inflation index for the same reason: neither currently reacts to market forces. Oil is manipulated by a cartel, which can kink the hose at will. You don't want that determining your cost-of-living adjustments and other policy decisions mechanically. Much better to break it out and deal with it directly as the economic attack that it is. And food is heavily subsidized. Attempting to gauge the economy by measuring food prices is religion, not science.
Because of the unemployment fostered by this change from a regulated economy to one racked by bubble after bubble, there's a lack of demand, a lack of production, and a downward pressure on prices. QE is backfilling that, while also offloading government debt and encouraging investments and innovations that are starting to show some employment pressure. Old industries may be improving their profits by hiring slave labor in China, but new ones are creating jobs here. When employment gets out of the scary zone (anything above 6%) we should see overall demand start to pick up, which will then start the inflation pump. That is when we should stop with the QE. If the Fed wants to modulate it to a finer granularity, that's fine, but it needs to guard against maintaining the status-quo. The economy needs a kick in the pants to get out of the well, not just a protruding root to dangle from while Lassie goes for help.