Why are the party slogans paradoxical?

The various slogans put out by the Party ("War is Peace," "Freedom is Slavery," and "Ignorance is Strength") are not just paradoxical; they are flat out contradictory. This is an example of what is called doublethink: the simultaneous conception of two mutually contradictory beliefs as being correct.
The purpose of doublethink is to keep the population firmly under the Party's control. Contradictory slogans encourage people not to think rationally about what they are being told. They are expected instead to uncritically accept whatever the Party tells them, however contradictory their messages may be. Slogans exist to be believed, not questioned, just like the Party itself.
If we examine a couple of these slogans, we can see how they are meant to work in practice. "Freedom is Slavery," for example, is a way of getting people to fear freedom and remain loyal to the regime. Things may be bad, the slogan appears to be suggesting, but the alternative is even worse. "Ignorance is Strength" is designed to make people feel good about allowing the Party to do all their thinking for them. The message here is that it is actually a sign of strength to accept every last thing the Party tells you.