1. What do you usually call a beautiful dress or suit which people wear to parties, theatres ....

evening dress / suit
party dress / suit

2. Can I say: "This dress is party." or "This suit is evening." ?

3. Neat / smart. Which word would you use in these sentences? Maybe there are some other words to describe beautiful clothes for parties?

This dress is too neat / smart. I need something more casual.
This dress is too plain for such a party. I need something neater, smarter.
For women, it is often 'evening dress.'
For men, "formal attire" or, if tuxedo is expected, "black tie."
Formal attire works for either.
Can I ask a man:

"Have you got an evening suit?"
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'Evening suit' is not a common phrase in American-style English, though, I am sure
the meaning would be clear to anyone.

Also, "have got" is not an especially highly regarded use of the verb, 'to have.'
Normally, 'Have you formal attire?' or 'Do you have a formal suit?' is preferred.
I was corrected on that by a counter attendent in Bermuda, where all the
natives speak English better than I do, when I asked, "Have you got hamburgers?"
"Have we hamburgers?" she replied. That was the last time I used 'have got.'

As for formal wear, in general, men are not expected to own true
formal attire, which means a tuxedo, today. During my working
career, I owned one but never wore it. Instead, I had a dark (navy)
blue (close to black) worsted that worked for just about any formal occasion.
The shirt should be white, and the tie a dark solid, black or blue.
Shoes should be black leather, preferably plain. The clothes should fit.

Another catch-all term receiving a lot of use now is 'black and white wear'
to mean formal attire for men.
Thank you, ed_shaw, for such a detailed explanation.

Do you know which word is opposite (antonym) to "casual"?

ex. Jeans are casual clothing, and evening dress is .......... clothing.
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Ed, where do you live? I've never heard or read the phrase "black or white wear" in my life, except for a local charity ball where nothing but black or white gowns for the ladies is permitted (true - I know a woman who thought she'd be daring and wear red but was turned away).

Also, don't let some Bermudan counter attendant shame you for using the perfectly correct "have got." Moreover, let us proudly clling to "gotten," which we Americans have so prudently preserved in amber. http://wiki.answers.com/Q/Is_gotten_correct_grammar