
I recently saw some of Hannah Biemold's oblique origamic architecture by way of the Evermore Origamic Architecture mailing list, and decided to have a go at the oblique technique myself. (Please pardon the flimsy paper and rough cuts - this is just a proof of concept)
The key, as Hannah mentions on her page, is making sure all of your fold lines converge at a single point, which I think needs to be on the main fold line of the card (although that point need not occur within the bounds of the card itself.)
Once you have the grid laid out, you can design just as you would a straight 90 degree card.
I like to lay card patterns out in Adobe Illustrator, but to get a better feel for designing oblique cards I drew this one by hand - here's how the back of the card looks without having erased any pencil lines:
It's especially interesting to see how the vertical lines of the folded card become distorted as the distance between the horizontal lines increases. With some experimentation it should be possible to figure out how to angle the vertical lines to compensate for some of the distortion.,