How can CP9 members and Sanji(post-timeskip) run and stand in the air? Do they use something like Haki? If not, what kind of techniques do they use? If it is Haki, can Luffy and Zoro run and stand like they do?
Actually this technique that Sanji uses is called Sky Walk it doe not use any haki, he just learned it by training while running everyday increasing his speed making him run in the air.
This is the aerial version of Blue Walk. Sanji kicks the air to jump higher, giving the appearance of flight. Sanji created this technique during his ordeal in "hell" to escape from the okamas. It was first seen used to escape after being surrounded by the Sea Urchin-Armor Spine Squad, making them hurt themselves. (Vol. 64 Chapter 635 and Episode 555)
As you can see he developed and learned this technique because of his ordeal during the time skip while training in Kamabakka Kingdom. giving him immense speed.
They are using one of the Rokushiki techniques.
Rokushiki is a special, superhuman martial arts style. In the Viz Manga and FUNimation dub, they are called the Six Powers
-- One Piece Manga and Anime — Vol. 37 Chapter 347 (p. 9) and Episode 245, Rob Lucci explains the Rokushiki.
The one they are using is called Geppo
The Geppo allows the users to actually jump off the air itself, allowing them to stay in the air for much longer than usual. CP9 members can use this technique to cross great distances without ever touching the ground, or set themselves up for swift, aerial attacks.
-- One Piece Manga and Anime — Vol. 36 Chapter 343 (p. 5-6) and Episode 242, Geppo is first used by disguised Kalifa.
As far as I remember, nothing has ever mention about how can Sanji and CP9 do this technique, but it's not haki. None of CP9 members are haki user.
One possible way to do this is they running so fast until they reaching considerable speed that they can put a step mid air, it first happen to Sanji when he was trying to run away from okama every day while training in Kamabakka Kingdom that he reach at a speed when he can do the "Sky Walk".
One other theory is it has the same principal with "Soru". This is one of the six techniques of "Rokushiki" that allows the users to move at extremely high speeds so people can't see with normal eye. It was revealed that the principle of this move was to kick off the ground at least ten times in the blink of an eye.