We report the discovery and analysis of the follow-up ROSAT pointed observation, an ASCA observation and optical and radio observations of the enigmatic Narrow-Line Seyfert 1 galaxy RX J0134.2-4258. While its spectrum was one of the softest observed from an AGN during the ROSAT All-Sky Survey, its spectrum was found to be dramatically harder during a pointed observation although the count rate remained constant. In the pointed observation we found that the spectrum is softer when it is fainter, and spectral fitting demonstrates that it is the hard component that is variable. The ASCA observation confirms the presence of a hard X-ray power law, the slope of which is rather flat compared with other NLS1s. Survey and follow-up radio observations reveal that RX J0134.2-4258 is also unusual in that it is a member of the rare class of radio-loud NLS1s, and, with R=71, it holds the current record for the largest radio-to-optical ratio in NLS1s. We discuss possible scenarios to explain its strange behaviour.