Subject verb agreement

[Unregistered]

Hi,

Please clarify me on this,

Which of the following two sentences is correct?

1. The judge did not believe any of their story
2. The judge did not believe any of their stories.

Also,

1. Each of the girl is intelligent.
2. Each of the girls is intelligent.

Also,

1. Some of the things he told was/were lie/lies.( which word should be used?)

Please cite the reasons behind the correct answers.

Regards

[David L.]

If this were a test, or a poll, I'd be glad to oblige. As it is, which do you think are correct and why? Then perhaps others will contribute if they think you are in error and need help to clarify your understanding.