Why are pronouns I, she, he sometimes used in a direct object position.?

It should be "Joe and me" or "John wanted to give us the money". If you said "John wanted to give me the money", that would mean something entirely different. What you should never do is use "Joe and me" as the subject, it would be "Joe and I". e.g. Joe and I received some money from John.

I hesitate to say that it's never correct because I'm sure that if I do, I'll think of an exception later. Those pronouns should not generally be used as objects.

What do you mean you were told to make it singular? You can leave "Joe" in the sentence.

You are right. People take the rule about "John and I went to the store" too far, and say that "John wanted to give Joe and I the money." What you really have to consider is just what you've said: you wouldn't say "John wanted to give I the money."

No I don't think its correct, but people say it often because they don't know any better. You're supposed to say I think "John wanted to give Joe and me the money" and someone might correct you to say I instead, but point out that it would be wrong to say "give I the money".

John wanted to give Joe and me the money.

You can have more than one pronoun for the direct object, but the pronouns for direct objects are "me, her, him."

Well I and me are both singular. Neither one of them are plural. It is correct to say Joe and me. Only use I when it is the subject. People tend to use I because they think it sounds correct.