OK. AFAIK, rule-wise, you only inherit the traits of one parent (so your half-moon, half-dark, elf, would be, rulewise, either a moon or a dark elf); but the appearance (and mentality) being up to you, you can make it a blend of both.
For the orc/elf hybrid, you can go the Arcady way and says that each aspect balance each other, and produce a being that is intermediate between elf and ork: human. Or you can create a new race for this hybrid. IIRC, there's an elf (wild or wood, don't remember) who got +2 Str, +2 Dex, -2 Con, -2 Int, -2 Cha. It could be a good basis, stat-wise, for an elf-ork hybrid. Then remove the "detect secret doors" and "+2 to Search" bonuses, and give him Darkvision 60 ft. For the appearance, imagine an hairy, muscular, elf with a big jaw, and here you go.
Edit: Note that in some world, Gruuuuuuuumsch and Corellon may not exist; and elves and orcs can have different mindset. Even if, by talking about "moon elf", the original poster implied it was in the Realms, don't jump to conclusion too eagerly. It may be a homebrew world with elves copied on those of the Realms, but who are not innately hostile to the orcs.