Yes, "party" is a noun. It has several distinct meanings:
"We're throwing a party for her birthday." — A planned event with guests, food, entertainment.
"She joined the Green Party." — An organized group seeking political power.
"The party of the first part..." — A person or group involved in a contract, lawsuit, or transaction.
"A party of hikers reached the summit." — A group traveling/acting together.
"A patrol party was sent out." — Small detachment.
"They partied all night." — To attend/enjoy parties.
Adjective: "Party dress," "party line," "party trick."
Context determines which noun sense applies.