We present a study of the X-ray variability properties and spectral shapes of five active galaxies all of which show extreme or enigmatic X-ray properties. We focus on QSO 0117-2837, RX J0134-4258, and NGC 4051, and briefly comment on Mrk 1298 and 4C +74.26. The individual objects were originally partly selected as candidates to host warm absorbers on the basis of (i) characteristic X-ray absorption features (NGC 4051, Mrk 1298, 4C +74.26), (ii) extreme X-ray spectral steepness (QSO 0117-2837; this object is found to be located in the 'zone of avoidance' when plotted in the Gamma(x)-FWHMH beta diagram), and (iii) drastic spectral variability (RX J0134-4258). The temporal analysis reveals large-amplitude variability by a factor similar to 30 in the long-term X-ray lightcurve of NGC 4051, very rapid variability of Mrk 1298, constant X-ray flux of the NLSy1 galaxy QSO 0117-2837, and constant mean countrate of RX J0134-3258 despite huge spectral changes. Besides the warm absorber, several further mechanisms and their merits/shortcomings are investigated to explain the spectral characteristics of the individual objects. Different models are favored for different sources. Consequences for Narrow-line Seyfert Is in general are discussed and we present results from photoionization models to distinguish between different suggested NLSy1 scenarios.