These three slogans are all quite paradoxical since they appear to be contradictory, yet hold a great deal of truth in relation to the novel. Remember that this is a Dystopian novel that takes place in a Totalitarian society where all personal freedoms, including the ability to think for one's self, have been stripped away.
Freedom is Slavery: With freedom comes the responsibility of making choices. In this society, people are usually punished for independent thinking or any type of behavior that is not dictated or approved by The Party. If people made their own choices in this society they would likely be captured by the Thought Police and vaporized. Freedom is slavery because freedom would lead to bondage and death in this society. You become a slave to yourself, a slave to the responsibility of thinking and acting on your own. By allowing the party to strip away your freedoms, you no longer possess the responsibility to think or make decisions and are "free" from the threat of capture and vaporization.
Ignorance is Strength: As mentioned before, knowledge and free-thinking will ultimately lead to being captured and vaporized in this society. By remaining ignorant you remain strong, because you are not a threat to The Party. If you possess knowledge as Winston and Syme did, The Party becomes threatened by your abilities. Having knowledge may lead people to question Big Brother and eventually attempt to overthrow the government. Ignorance is strength, because it keeps you alive and safe from the threat of capture and death.
War is Peace: The people in this society need somewhere to direct their anger which is why The Party invented Emmanuel Goldstein. If the people do not believe that Oceania is at war and threatened by Emmanuel Goldstein, they will start to question the conditions they are living in and the laws established by the government and eventually direct their anger towards Big Brother. War is peace, because war unites the people of Oceania and maintains harmony within that particular super-state in order to avoid the threat of mutiny.