What is the formal term for energy in Dragon Ball Z? In Bleach, the term is "reiatsu". In Naruto, it is "chakra". However, all I ever really heard in DBZ is "power level". Is there a more formal descriptive term for the source of their powers or the energy they give off?
The original Japanese term is ki (pronounced the same as "key", written as 気). It can also be spelled chi or qi. The same term is used for a concept in martial arts, though naturally Dragon Ball's version is quite a bit different from this. In the English dubs, this term is never used, and "energy" is used throughout the series.

According to Toriyama, there are 3 components of ki, namely Genki (元気, roughly meaning Energy), Yūki (勇気, Courage), and Shōki (正気, Mind). Ki also can be positive or negative. The various charge up and transformation sequences are all done in order to increase one's ki.

Dragon Ball Wiki has more information on ki in the series.