As quasars are the most distant objects in the night sky, they are therefore subject to the greatest speed of recession. Is it possible, therefore, that the weird measurements we obtain for their energy output and size could be a result of relativistic effects rather than being intrinsic to their natures?
The measurements which are reported for quasars are already corrected for redshift and other relativistic effects. An assumption which is occasionally used the calculations of total energy output, however, is that they emit all their radiation "isotrpically." That means we assume the same amount of energy is radiated in all directions. Quasars, however, are probably the result of high-energy jets from supermassive black holes which happen to be pointed directly at us. If we were to view the same object from a different angle, we would not observe the same high energies. Clearly, such jets are not isotropic. Therefore, isotropic energy estimates for quasars are probably vast overestimates. Astronomers understand this and try not to compare such estimates to other phenomena. Eiter way, though, quasars are some of the most energetic objects in the sky.
Edit by Michael Lam on February 10, 2016: For a more numerical answer, they can be 10-1000 (or more!) times the luminosity, the power output, of the entire Milky Way.