Nothing runs when phone is hard off, not the OS not batterygraph.
Note, however, that the phone is NOT off if it has power via USB, be it charging or connected to a PC or whatever. It boots to a minimal stage, where daemons like BME start but no user login (IIRC). If it is charging and "off" then the CPU might as well be at 50% for what I know but it's likely that in that stage data about load is not available.
Anyhow, back to the point. There is no CPU when phone is off. Also, please use either batterygraph or the commandline to see voltage of battery when charged completely. (x-term command is "lshal | grep battery").
You might have a feeble battery, as suggested. Oh, and, get cpumem-applet. It offers insight on CPU load all the time. Once it seems to not go down, use top or conky to see the troublemaker.
Also, how many images, videos, sounds do you have? A bad/lot of media can have the tracker track for hours.