Robert Sasata is correct, there are clearly two species here. Besides the Kirchmair et al paper he sites, also see:

Kirchmair, M., Pöder, R., Huber, C.G. & Miller Jr., O.K. (2002). Chemotaxonomical and morphological observations in the genus Omphalotus (Omphalotaceae). Persoonia 17(4): 583-600.

This was discussed in Kirchmair et al. (2004) “Phylogeny of the Genus Omphalotus Based on Nuclear Ribosomal DNA-Sequences” Mycologia 96(6):1253-60. Phylogenetic analysis clearly shows they are different species, despite the outdated opinions of some authors, who could not even agree on the characters that separated the two.

Hmm, I am not sure if the two names represent different taxa (O. olearius is a European name, while O. illudens is an Eastern North American name), or if they are synonyms; in which case I wonder which is given presidence.

IndexFungorum still has the two taxa split, and Agaricus olearius was described in 1815, while Agaricus illudens was described in 1822.

So if they are synonymous, I would like to hear the argument for why the older epithet (O. olearius) should be deprecated in favour of O. illudens.