Me vs I vs myself

Massimo Scola"The only people at the party were James and myself?"

No. The reflexive pronouns are only to "reflect" the earlier use of the same pronoun.

I can do it myself. (I ... myself)
Look at yourself! You're a mess! (you ... yourself)

That being said, you will hear the reflexive pronouns used out of place in casual conversations.

Massimo ScolaIs it correct to say "The only people at the party were James and myself?" or would you write/say "The only peoples the party were James and me?" .. or "James and I?"

The easy way to answer all questions like this is to remove the other noun.

The only person at the party was me.
The only people at the party were James

Purists: James and I
Realists: James and me
Wrong: James and myself
[ It seems that recently myself is gaining in popularity, even as a subject pronoun, but this use is incorrect. The -self pronouns are reflexive pronouns and should be used as such; they are also used for emphasis. I, myself, don't like that shirt on you. He thinks a lot of himself. ]

PhilipIt seems that recently myself is gaining in popularity,

I notice this too. Some people seem to feel that changing "I/me" to "myself", whatever the context, somehow makes the sentence more sophisticated or polite.

GPY somehow makes the sentence more sophisticated or polite.

That's exactly what I attribute it to.