Hamlet's hyperbole . . .

First thought is it isn't out of character - it is very much within a view of Hamlet as far from perfect!

It clearly shows that Hamlet has unrealistic views - that he will use language as a weapon against others and that 'rhetoric' is to the fore in all he says: How can anyone trust what he says?

Interesting the comparrison with what the prologue says about Henry V.

How are we to judge Hamlet's words? Clearly he is idealizing his father and his marriage but why is he doing so? Is he delusional? Not only is it not persuasive, but it seems out of character, can he truly believe what he says?

I like this question a lot. I hear similar ideas from him in the 'piece of work' speech and a little in the graveyard scene, though they are not about his father. Assuming it is supposed to make sense, and to the question of whether he truly believes what he says, perhaps he is more painting pictures for contemplation than expressing some definite belief of his own. I do a similar thing when juxtaposing perspectives in my mind. The images are there merely for rational entertainment, and the analysis is easier when the properties are exaggerated or simplified. This makes more sense for the 'piece of work' speech than for the ones you mention, though.

When talking to his mother, he could be exaggerating to make his point. Presumably, even if she disagrees with his extreme characterizations, he could get her to admit to some difference between them, which is a start.

In 'too too sullied flesh', he is in distress, which makes exaggeration natural. I have seen people who are recovering from a loss look back at their lost relationship as better than it actually was. I haven done it myself. It seems like a natural human reaction or phase. His idealizations could also have come about gradually, as a reaction to, or a kind of overcorrecting for, the lack of reverence, respect, love, mourning, etc. that he perceives in the court around him.

Perhaps the excessive aggrandizing has many roots.-- Dramatic antithesis to his feelings about Claudius--"Look you now, what follows:"--for the benefit of his mother's understanding something about what is to her his irrational--nay mad-- behavior. He doesn't tell her what he's been able to confirm, only moments before, about who he next describes; he's forced to explain the magnitude of his feeling without being able to explain it at all. And let's remember too, how he regards women--especially one with the series of (in his estimation) careless emotional leaps his mother has made recently. Perhaps this is the only way he thinks he might be able to really communicate with-- get something of his message across to her. In any event, as usual, he's hamstrung by circumstance and events--which is why, I believe, he thinks aloud so damned often. He speaks to himself even as he is speaking to others.
And what we say to ourselves in times of great stress is too often proved later on to have been, shall we kindly say, somewhat inaccurate.