The makers of USMLEWorld have made several changes to the website to make it difficult to access via Mac. At one point, I was able to use Firefox with a free extension that caused the browser to masquerade as if it were IE5 on a PC. When this quit working, I switched to IE5 for Mac. For a while, it was possible to make a small change to the binary code to masquerade as IE5 for PC. However, that, too, eventually started malfunctioning, apparently due to further changes on the USMLEWorld website.
I haven't tried the OMNIWeb browser, but I'm skeptical that it would work, given that the hacks mentioned above no longer work.
Though I haven't tried it, Virtual PC probably would work. This is a program that turns your user-friendly Mac into a slow, unstable PC running IE5. This is an expensive approach but is unlikely to quit working due to changes to the USMLEWorld website.
By the way, the reason the makers of USMLEWorld disable access via Mac is because they are concerned about copyright violations due to copy-paste operations, which they are able to disable on the PC but not on Mac.