Keep in mind that cross-tolerance is almost always going to play some part in finding the correct dosage of a new Opioid analgesic. You can try to calculate this beforehand, but it's really difficult to do so, as people have widely varying metabolisms and certain drugs affect certain people in drastically different ways.
With that said, 1mg of Oxycodone PO is roughly equal to 0.5mg Oxymorphone PO. So, we know that Oxymorphone by mouth is approximately twice as strong as Oxycodone by mouth. Now, we also know that the oral bioavailability of Oxymorphone is a meager ~10%. With that in mind, we know that almost all drugs are 100% bioavailability if administered by the IV route. IM/SC injection ranges anywhere from 85% - 100%.
Doing the math and knowing that Oxycodone's bioavailability, whether by mouth and by injection is not drastically different (~15%), we can say that 1mg of Oxymorphone IV is equal to ~10mg of Oxycodone by mouth. If I have fucked up this math somehow, please rescue me someone. I'm kind of out of it at the moment. Anyway, the moral of this story my friend, is that if you have the notion, you can really exploit Oxymorphone drastically variable bioavailability. Your oral dose, whatever it may be, is multiplied by ten.
If they give you the 10mg instant release pills, they are not difficult to prepare for injection, although you should always use a micron filter - especially with pills - and clean water. If they are the extended-release, with the newer version of abuse-proof tech, then you really should not inject these. It's possible, but there are a lot of reports of people seriously injuring themselves and the common thread was specifically, injection of extended release Opana. All pills are dangerous to inject, but these are apparently quite harmful in comparison to other pills.
So yes, you can get much mileage out of your Oxymorphone by using the IV route, but if you ever end up in say, the hospital, you'll have someone administering your drugs to you every day by mouth and it might be hard to do what you need to do. Also, you don't want to become dependent on high doses of Oxymorphone, so I would really reserve this practice to a sporadic frequency, like when your pain is really bad.