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Actually the slogans are more like paradoxes.
There is a lot to this but here is a simple explanation,
War is Peace- While the country is fighting, people within the country are on the same side hence the Party enjoys uncontested power. Nobody questions their government while at war...It's that sort of thing.
Ignorance is strength- If people remain ignorant, they will not question the Party hence making the country "stronger".
Freedom is slavery- If people are free to do things and express ideas contrary to party doctrine, everybody is made weak. They are slaves to their own ideas and not strong under one idea from the Party.