Morphine - Basically like heroin, but much weaker and takes way longer to come on, although I have only ingested nasally and orally, the rush I am sure is different when IV'd. You do get that warm euphoria, but I wouldn't say the rush is anything amazing, but definitely works when you can't find anything else the get high with.
Heroin - WOW! THE ULTIMATE RUSH! I also recently IV'd for the first time and I can't believe I waited so long to do so. You feel that warmness throughout your entire body, your head spins but in a good way, vision goes blurry, instant desire to nod. I would rather have and IV dope rush than an orgasm... nothing in the world compares.
Oxycodone - A lot of people compare this to dope, but I find severaly distinct differences. While you do get that blurry vision and warm euphoria, the rush is far more speedy. You almost get this overwhelming God like feeling... kinda like you can do anything you ever dreamed of. The rush of Oxy is more of a speediness than noddiness.
Hydromorphone - I would say this comes on rather slow like Morphine. Also produces that warm euphoria, but no blurry vision or dizziness, although it should be noted that I have only plugged and sniffed, never IV'd. The high is also much shorter lived than all of the above. I would put the rush one step ahead of Morphine, but the high is definitely at the bottom of the list.