What power does the individual hold/yield in society in the novel 1984 by George Orwell?

The individual in 1984 has no power, as Orwell intended it. The people of 1984 live under a totalitarian regime with "Big Brother" as the head of state. The often-quoted "Big Brother is Watching You" slogan plastered throughout the novel emphasizes that individuals have no privacy, and no control over this fact. Everything about the 1984 society is aimed at subjugating the masses--instilling in them an unparalleled sense of fear, loneliness, and powerlessness. By doing so, the government is able to control the individual--their marriage, their children, their lifestyle--all while leaving the individual as a helpless pawn of society.
The theory behind it being that frightened citizens are unable to unify and overthrow the government. If everyone believes (and has it instilled within them) that they are unable to make their own choices and are continuously monitored, they are essentially trapped and unable to escape--just like mice in a maze.

The individual has no power whatsoever in the dystopian world of 1984. The state of Oceania is a brutal, one-party dictatorship in which basic human rights are routinely and flagrantly disregarded. Every aspect of life is controlled by the Party, including the inner life of its citizens. The regime uses various methods of mind-control to keep the population firmly in check. It's not enough that the Party controls what people do and where they go, but also what they think. In Oceania, your life is not your own; it belongs entirely to the Party.
That said, the Proles enjoy some measure of freedom, relatively speaking. The regime doesn't regard the Proles as having much in the way of revolutionary potential, so they're pretty much left to their own devices. Unlike the rest of society, they don't have to have intrusive telescreens in their homes to keep them under surveillance. They can also engage in sex whenever they like and are free to get a divorce, a privilege denied the rest of society.
The Party cynically believes that if the Proles are kept in a state of ignorance, fed on a constant diet of cheap booze, mindless entertainment, and pornography, they won't get any ideas about overthrowing the regime. This may not sound like much of a life, but it's the nearest that anyone gets to freedom in this totalitarian society.