I am a native American English speaker, and I would not expect them to sound the same. Why would they?

However they are both unusual and unfamiliar, so people might get them confused anyway.

"Oryx" is pronounced "are-ricks". Doesn't sound like "our ox".

Depends on accent. In my NZ accent, "oryx" doesn't sound much like "are-ricks" at all. To me oryx and aurochs sound similar enough I can imagine people confusing one unfamiliar hoofed animal for the other.

For me "oryx" does sound like "are-ricks," but "our-ox" is basically indistinguishable from "are-rocks." Only the one slight vowel sound of difference.

Thanks to you all, for your answers!