These three phrases seem to ring true in many different ways. Aside from the connections made above, the phrases could also be seen as a cruel in-joke on the government's part.
Although they bombard the stricken masses into belief,
to no-one are the phrases truer than for the government itself.
War is Peace:
When a nation is at war, with the whole population geared behind war effort, as in 1984, who is more at peace in their position than the leaders of the country. If the leaders have acted cleverly enough they will have directed their population's anger towards 'the enemy'. It is therefore less likely that a disgruntled citizen is going to attempt to overthrow the government than if it were a time of peace, and the disgruntled citizen had no-one to blame but the nation's leaders. So, to the leaders, War Is Peace
Freedom is Slavery:
When the population of a nation is enslaved into serving their government, the only ones with freedom are the leaders of that government. First of all, if properly enslaved, the population is too busy serving the government to stop them doing anything, and secondly, the leaders don't have any work to do, leaving them free to do as they please.
Ignorance is Strength:
If the population does not know that anything more can exist, or that they are being lied to, or that change is possible, they aren't going to care. If a government can manage to keep it's population so ignorant that they do not question what they are told, no weaknesses within what the government says will ever be found.
In summary, when is a body so strong as to be free to do as it pleases in peace than when it's minions are ignorantly enslaved into war