In one all elf party, racial superiority became an in-joke, and the elves referred to humans they met as 'breeders,' because that's all they seemed to do. Much sniffing ensued and talking of how elves didn't have litters of children, since they were further removed from dogs and pigs than humans. Quantity over quality, and all that.
Get used to words like hoi-polloi and declasse and phrases like, 'mind your place' and 'do not interrupt your betters.' Do not go so far as to say something patronizing like, 'Shush now. Mommy's still talking to the nice man,' as that would imply that the lesser race is actually related to the speaker. That won't do at all. Say instead, "Shh. Quiet time. The grown-ups are trying to make a plan, now. Go eat something." Pause. "Just not anything of mine." or "Go read something." Pause. "Assuming you know how." or [pointing at the warriors sword] "Go play with your toys, now."
Insulting people in other languages is the best way to express contempt. Feel free to make up some elven-sounding words for 'breeders' and 'beast-men' and 'lowbrows' and 'common,' expressed with as much dripping scorn as you can muster, so that even if the other characters don't know what you just said, they'll know it wasn't nice. Feel free to mistranslate, with extra sarcasm. After calling the dwarf a 'rude unfinished foul-smelling toadstool' in Elvish, explain to him that you just said that his idea was simply marvellous, and that the party was assured of a glorious end if they followed his oh-so-clever tactic.
Always make a point of not mentioning the race of non-elves, and always mangle their names. Introduce yourself with a grand name, many titles, heritage, etc. Introducing the dwarf, *only* after being reminded to do so, point and say, "Oh? That? Brack, I think." "Brok!" "Yes, whatever." When his race is mentioned, even if you've been told a million times, "Dwarf?" [look at obviously dwarven companion askance] "I suppose. They all look the same to me. I thought he was a Goblin with some sort of facial growth. A tumor perhaps. You know how they are..."
Similar to the Thurston Howell reference above, I modeled mine off of Charles Emerson Winchester, from M.A.S.H.
"Hey, how come you aren't sweating?"
"Winchesters do not 'sweat,' they perspire. And *I* do not perspire."