Individual is loosely overused to refer to "one person only" and often has a humorous or contemptuous meaning: "Who is that individual with the loud mouth and wide grin?" Except in legal and telephonic language, party is not recommended as a reference to one person. Party refers to a group (a supper party, the Socialist party) and is dubious in a sentence such as "Who is the party that brought you to the store?" In most situations, person should be preferred to either of the other two terms when reference is being made to one. Phrases such as "individual person," "each individual member," and "individual self" are wordy.
Dictionary of problem words and expressions. Harry Shaw. 1975.