At first glance, these slogans seem to be contradictory and illogical. And, they pretty much are, but the society in 1984 is run by a group of people that have pretty much brainwashed or intimidated the entire population into believing whatever sort of nonsense they promote. So, these three slogans are lived by and sworn by, and the essence of everything that the Party represents. Each of these three slogans have double meanings--one for the Party and one for the people as a whole.
First of all, let's look as War is Peace. In their society, keeping the masses believing that constant war is being waged is actually a way of maintaining peace. War elicits great patriotism and devotion to country; it also promotes sacrifice and giving to the community over oneself. So, if there is constant war, the people are constantly giving, sacrificing, and pledging devotion to their government. This keeps the people in check and in control, and hence, peaceful. That is how the Party uses that slogan. The people think it just means that world peace is maintained through war. Without war, their security would be threatened.
Freedom is slavery is more tricky. The people probably believe that to mean that having total freedom is actually a way to become enslaved to your senses, weaknesses and vices. For example, the Party encourages young women to remain virtuous and restrict themselves from being romantically involved or sentimental in any way. The society has firm beliefs about sex and relationships--there is very little freedom there, because they feel that sex and relationships enslave people. If you are constantly embroiled in relationships, you are subject to the turmoil and unhappiness that they sometimes cause, and are constantly thinking about it. That is not freedom, according to them. So, to the people and the masses, they have been taught that freedom to act, and sometimes act poorly, actually tends to enslave one to sentimental and unessential vices and emotions. To the Party, a free people represents the removal of their power. So, the people must not be free in order to remain in power.
To the masses, being ignorant about the true condition of things is actually beneficial, because it helps them to remain happy and optimistic, and thus strong. To the workers within the Party, like Winston, their entire jobs rely on keeping the people ignorant of true facts and statistics. Essentially, lie to keep the people in the dark, and then the Party--and their jobs--will always be strong. The people's ignorance gives the Party strength; if they really knew the true state of things and how they had been manipulated, they would rebel, and take away the Party's power.
In the end, it all comes down to the Party creating slogans that ensure the continuation of their power and control. I hope that helps; good luck!