What are the words useful in a party in Japan?

It depends on natures of parties, but the three major good Japanese phrases useful in a party are:
1) Onemaki-itadakimashite, Arigatogozaimasu.
Meaning, "Thank you for inviting me to the party."
2) Anatano-sorewa, katsura-desuka?
Meaning, "Is it your hat? (Beautiful.)" "Anatano-sorewa, ........-desuka" is a useful phrase you can use in a formal party. If you put "icchora", you might mean "How nice your suits is?"
3) Anatano-kaowa, totemo-hendesu.
Meaning, "you are very unique." Pointing uniqueness is the thing Japanese people think the best admirable description among the most Japanese think themselves ordinal. So, if you tell someone this, he or she will receive it as if you admire him or her.
Please try those to make more friends in Japan.