The powers of the Fantastic Four are: based on the classic elements, air, earth, fire and water. The powers are assigned as an element of their overall personality or psychological profile. There is nothing ironic about how their powers relate to each of them.
The Human Torch's fiery, risk-taking personality is reflected in his becoming a being of flame.
The Invisible Woman, as was the wont of women in the 1950s and 1960s, was culturally invisible and thus her powers reflect this state. Sue Richards is air, she becomes invisible, like the air, and can manipulate the "air" to create fields of force, which are also invisible.
Ben Grimm, a figure of strength and determination, became a Thing, forged of rock and earth.
Reed Richard, a being with a plastic and fluid mind, capable of encompassing anything the world has to offer, becomes Mr. Fantastic. He is protean, in the classic sense of the word, he can change his shape and fill any container, much like water does. See a further expansion on Reed Richard's powers.
Their first origin as depicted in Fantastic Four #1:
Classic Elements in Popular Culture (Wikipedia)
In the comic book series Fantastic Four, each of the four characters have powers which relate to the Greek elements. The two most obvious links are the Human Torch (whose fire control power is best expressed through the image of him as a burning man) and the Thing (who resembles a living being of rock and stone).
Mister Fantastic, while not having water-based powers, does have a fluid form. The Invisible Woman's powers of invisibility and force fields evoke the unseen forces of wind and air. This is especially true in Neil Gaiman's Marvel 1602, where the Invisible Woman is both permanently invisible and weightless.
It should also be mentioned the two obvious elemental personalities (the Human Torch and the Thing) tend to have personality traits people tend to associate with their own elements. Johnny the human Torch is impulsive, quick to anger with a brash personality, contrast this to Ben the Thing who is more sullen, dependable and strong.
This was not an ironic assignment of powers. Ironic would imply each ended up with powers opposite of their nature.
i·ron·ic: adj; using or characterized by irony; happening in the opposite way to what is expected, and typically causing wry amusement because of this.
Synonyms: sarcastic, sardonic, cynical, mocking, satirical, caustic, wry, paradoxical, incongruous
"His mouth curved into an ironic smile."
"Edward's tone was ironic."
"It was ironic that now that everybody had plenty of money for food, they couldn't obtain it because everything was rationed."
"It's ironic that a former illiterate is now a successful writer.