I have Khajiit and Argonian. It doesn't feel strange at all because they both fit with the story. Why should it be only a Nord who is Dragonborn?
Surprisingly though, Khajiit often live on the edges of society but thee two places I would expect to see more Khajiit is in both the Thieves Guild and the Dark Brotherhood but if I recall, neither of them have a khajiit member. Also, only the Dark Brotherhood has an Argonian, the Thieves Guild does not.
The DB has plenty, you just don't get to talk to them. On my Orc character alone, I've been attacked by over 10 DB assassins, with 4 being Khajiit females, and 3 being Argonian females. The rest were Dunmer, lolz. Also, my female High Elf mage has been assaulted by around 8 DB assassins, with similar demographics to the ones attacking my Orc. As long as you just keep traveling the roads and do NO Fast Travel, they'll keep throwing themselves at you. It's quite entertaining actually...though very pathetic on Astrid's part.
I find it great that if you just keep playing without getting into every guild, the game is more mysterious and interesting for you, because the guilds seem more powerful and exclusive. I know this because my main character is in them all, and it seems really ridiculous....just like in Oblivion.....