Why Did Itachi Join Akatsuki?

He joined the infamous criminal organization Akatsuki to see that they do not plot any harm against the Hidden Leaf. He destroyed his own reputation and even took on the burden of Sasuke's hate in the hopes that it would make him stronger.

Why did obito let Itachi join Akatsuki?

Because he wanted Sasuke to kill him and awaken his powers and control Sasuke after that because he is easily brainwashed and anger revenge driven.

Who forced Itachi join Akatsuki?

Itachi, as a character, is so well developed in Naruto, that there are several layers to his actions. Alone, he hoodwinked the rest of the world, in order to make it a better place. The Elders of the Leaf Village did order him to infiltrate the Akatsuki and serve as their spy, true.