If you're willing to bide your time, the best bet is to finish the Companions quest line.
Once you do, any member of the Companions - including Nadja - will agree to accompany you as a follower.
Which means you can take her to a nice secluded shack in the middle of nowhere, and then take her out.
If you don't have the patience, or prefer a more...
public method, I'll refer you to questions like this one .
Essentially, raise your Sneak, (and optionally pickpocket or weapon) skills, wait for the right moment, and strike when nobody is looking - this will take some practice, and a bit of skill, but it's good training for the Brotherhood after all.
gaming.stackexchange.com/users/3129/LessPop_MoreFizz
Complete the Companions questline, then take her as a follower and go to the Sacellum of Boethiah .
You need to sacrifice a companion to summon a Daedra.
She sounds perfect.
gaming.stackexchange.com/users/16164/jacobjfoley
This is a very funny way to kill her.
Just cast fury on her and the people around her will kill her for you.
Simple as that.
Hah, I paid Athis for lessons on one-handed weapons, and leveled up my one-handed skill.
Then I casted fury on him and guess what???
Everyone got out of there beds and started to kill him.
I was helping kill him too, and no one came after to kill me.
Hah, pretty smart.
Lol.
gaming.stackexchange.com/users/18375/Kyle Kern
Make sure you can get to the throat of the world.
Go to the VERY top.
Bring her with you.
Fus RO DAH!!!
gaming.stackexchange.com/users/30894/Nonna Urbuisness
I did it using sneak and arrows.
The first arrow did not kill her.
The Companions were mad, but I hid the bow and they relaxed.
The second shot did kill her, and I ran.
I went to a guard and he said nothing.
I came back, and they are OK with me.
gaming.stackexchange.com/users/5624/IAdapter
After completing the companion's quest line, I took the non-essential, and quite annoying companions to the underforge and slaughtered them, 1 - it gives you a cool cutscene, and 2 - impossible to get a bounty as it is only the two of you.
gaming.stackexchange.com/users/18221/D.B.Assassin
I was in The Companions house and Njada was very rude too me.  It's OK to be rude in this kind of game, but I would really like to kill her.  How do I do it, so that I won't have to kill the whole town?  Should I just kill her and run?  Could I then comeback and pay some big fine?  I bet she is useless in the main story and it would be a cool role-playing thing to do.
How do you kill one of The Companions?
gaming.stackexchange.com
<the-elder-scrolls-5-skyrim>
gaming.stackexchange.com/questions/41735
gaming.stackexchange.com/users/5624/IAdapter
Finish the Companions quest line and take her as a follower. Cast fury on her and others will kill her for you. Under certain conditions, you can kill the companion in question. The most common way to do so, is by completing the companions quest line and then proceed with any method of choice.
The community details different ways to kill the companion.