EDAX is a name of a company, abbreviation for technique is EDX or EDS. It's strength is identifying composition of small volumes (it's microanalysis). For bulk specimen analysis other techniques could be better.
From a quick perusal of some first-page google results, EDS is often applied through scanning electron microscopes, and gives you a "reasonably good" estimate of "all the elements" present at each location scanned by the electron beam. Otoliths are frequently developed with growth rings, so if you are wanting to identify when conditions changed, or a particular element started accumulating (or was no longer accumulated), this is the method you want.
On the other hand, ICPMS analysis will tell you "quite accurately" how much of each element you have calibrated your instrument for, but as an average of the entire sample.
Note that "reasonably good", "all the elements" and "quite accurately" are still dependent on the preparation of your sample, instrument and the level of accuracy you require. Both techniques suffer matrix issues and are destructive (no sample left after analysis), so choose the method that suits your needs.
EDS is generally used to obtain qualitative chemical analyses of elements present in the samples. Even if it is less comparable with ICP- OES, it also can be used to provide quantitative elemental analysis. ICP-OES can be used for the quantitative elemental analysis in a wide range of sample matrices due to its relative simplicity, flexibility, low cost, and low detection limits.