Does Arya not wield Valyrian steel?

Also Jon Snow has a sword but Robb Stark does not?

I think Robb inherited his father sword

Rob *should* have gotten the sword, but Joffrey did not allow for that to happen.  

The name "Ice" is a legacy from the Age of Heroes, and predates the current sword. About four hundred years before Robert Baratheon's reign, the Valyrian steel greatsword was spell-forged in Valyria and acquired by the Starks, who named it after that legacy.[2] It became the sword of the Lord of Winterfell. Eddard Stark used the sword to personally execute condemned prisoners. After his capture, Ilyn Payne was given the sword and used it to execute Eddard himself.[3] Ilyn carried the blade for a short time until Tywin Lannister took it from him and had Ice re-forged into two longswords, Widow's Wail, and the longsword later called Oathkeeper. -http://awoiaf.westeros.org/index.php/Ice

Derp. I should have figured the Lannisters wouldnt have just given it back.

Jared, thank you for the clarification! For bonus points please answer the Arya Stark sword question.

Also above it says Oathkeeper is owned by Brienne of Tarth, not Tywin. Is that right?

no

http://awoiaf.westeros.org/index.php/Needle

yes

http://awoiaf.westeros.org/index.php/Oathkeeper

Ah! So Tywin has Oathkeeper made, and then Brienne of Tarth ends up with it.

Does Jaime Lannister have any Valyrian steel?

not anymore, no sir

READ THE BOOKS

How do you remember all the details from the books???

1) I do not.  But yay internet!

2) I have read them many times.