Oryx are tough and they tend to be in open country. They can be tough to sneak up on. 300 yard shots are not uncommon on Oryx in the Kalahari or at White Sands in NM which is very Kalahari like.
I killed my 38" bull At White Sands NM in 1995. I shot him at about 150 yards with .30-06 using 180 TBBC bullets. The first round broke his on shoulder and double lunged him. he went down at the shot then got up and tri-podded for about 200 yards before going down again . I had to shoot him twice more to kill him. They are TOUGH. I guided my brother on his in about 1998 he also used the 180 gr TBBC in a .30-06 and killed his at about 75 yards on the run placing two bullets within about an inch of each other off hand as I've seen him do so often on running game at various unbelievable ranges. It's uncanny I don't know how he does it.
The Oryx is one of the few antelope in Africa which lions will steer clear of as a lion generally can't beat an oryx in fight. There are documented cases of one or two lions being killed by a single oryx in mortal combat. They are to be taken very seriously when wounded. A wounded cornered oryx is to be considered highly dangerous. Men have been and continue to be killed by these "swordsmen" of the Kalahari when approaching one that is not dead yet do so from behind never walk up to a downed oryx from the front. Even if you think it's dead better safe than sorry.
To answer your question about rifles here is where a good 180 gr bullet out of a .30-06 or a .300 mag are about prefect. Of course the various .338's using 225 gr or 250 are a very sound choice as is a .375 shooting 270 gr bullets. A 7MM using good 160 gr or heavier bullets would work just fine as well. Just keep your max distance to about 300 and you'll be fine. I wouldn't shoot further than this as these are big tough critter that take alot of killing and very precise shot placement.
If you shoot an oryx behind the shoulder you have gut shot him. you MUST shoot them in the shoulder putting the bullet in line with the front leg. Oryx are built like no other animal I've seen besides a Giraffe. Thier lungs sit on top of their heart and forward of the shoulder line. Their diaphragm is located directly in line with the back of the shoulder line. If you shoot them with a North American type placement behind the shoulder you have just messed up big time.
Are you hunting them in America or Africa?
In WSMR, NM you'll be hunting Oryxia Oryxia Kalahari which is I believe the largest of the oryx. In Africa you may well be hunting the fringed ear oryx which is a bit smaller in body and horn. On a game ranch in Texas you could be hunting the scimitar horned oryx which is now extinct in the wild as far as I know. There is one other type of oryx as well which I can't remember at the moment but I wouldn't think it important. They are all tough.
Good luck.