The cards are 3.5 inches by 2.25 inches (slightly shy of 9 mm cm by 5.75 mm cm). It seems to me that the copious amount of shuffling in this game might make it worth sleeving the cards, but I probably won't. I like the feel of the nice linen stock, and if I play it enough to wear out the cards, I'll just buy a new set--the designer and publisher will have earned my repeat business!
Edit: Wrong units for the metric dimensions--thanks for the correction, Russ.
The Onirim cards fit really loose inside the Mayday 'Euro Game' sleeves (the light-blue Dominion sleeves @ 59x92mm).
They should fit exactly into those 'USA Chimera' sleeves, although that means the card will fill the sleeve exactly. Any deviations in the sleeve width will curl the cards, and they will fill the sleeve all the way to the top when usually there's a little extra room there. Maybe they'll still fit in the original box with those sleeves?