Using data from the ASCA X-ray observatory, we examine the variations in the X-ray spectrum of the supermassive star eta Carinae with an unprecedented combination of spatial and spectral resolution. We include data taken during the recent X-ray eclipse in 1997-1998, after recovery from the eclipse, and during and after an X-ray flare. We show that the eclipse variation in the X-ray spectrum is apparently confined to a decrease in the emission measure of the source. We compare our results with a simple colliding-wind binary model and find that the observed spectral variations are consistent with the binary model only if there is significant high-temperature emission far from the star and/or a substantial change in the temperature distribution of the hot plasma. If contamination in the 2-10 keV band is important, the observed eclipse spectrum requires an absorbing column in excess of 10(24) cm(-2) for consistency with the binary model, which may indicate an increase in (M) over dot from eta Carinae near the time of periastron passage. The flare spectra are consistent with the variability seen in nearly simultaneous RXTE observations and thus confirm that eta Carinae itself is the source of the flare emission. The variation in the spectrum during the flare seems confined to a change in the source emission measure. By comparing two observations obtained at the same phase in different X-ray cycles, we find that the current X-ray brightness of the source is slightly higher than the brightness of the source during the last cycle, perhaps indicative of a long-term increase in (M) over dot not associated with the X-ray cycle.