Interesting thoughts. A non WotC publisher put out a Book of Drow, and in it they had examples of Drow/Orc, Drow/Goblin, and even Drow/Ilithid couplings. And yes, the Drow/Ilithid is just as disturbing as you're thinking it is.
I have to agree with 1st and 2nd editon, though, and say that Orcs and Elves, of any type (Grey, Gold, Sun, Aquatic, Deep, etc.) are incapable of producing anything but pain and suffering when coupled.
The Dwarf/Human thing is interesting, but I've never seen it done anywhere (officially) outside of Dark Sun. DS had some WEIRD races, and a Mul was just one of many. But it wasn't a viable offspring, because of their sterility. Halfgiants, on the other hand, were viable, but could only breed with eachother, because they had been magically created, ages ago. (Probably at the end of the Green Age, but I'm no historian.)
As usual, if your GM does't say "Not in MY Campaign," then you're golden, but I surmise that most will agree with the earlier editions and forbid it.
Oh, and I can't give you a quote about the Elven and Orcish creators, but at least in Greyhawk, the Elvish and Orcish gods not only dispised eachother eternally, the Elf plucked one of the Orc's eyes out. If either of them would overlook a hybrid child, I would be damn suprised. Hatred runs thick in the blood.
The Tolkien idea of elves and orcs has, as far as I've seen, been weaned out of D&D as of late. Orcs are generally seen as a rather bestial, yet related (sub)species of Human, seeing as they can couple and produce viable young. They have their own history and creation story, but as I follow the D&D Theory of Evolution, (Darwin would spank me for this,) I'm fairly sure Orcs are more related to humans than they are to Elves, sharing a later common ancestor.
- Kemrian the Xenobiologist