Beautiful space. Put the cushions/rug down first and then make a decision about the white curtains.

Lovely space! We had a similar porch, and I hung cheap bamboo roll-up blinds when I wanted full privacy (say in the evening), and also the fine cotton or muslin panels (Ikea) that I could close during the day, to allow plenty of light but detail was thoroughly diffused. It made for a really pleasing mix of textures, and was very inexpensive and easy to diy. And all washable!

Do you think it would look odd to just put curtains on the right side? The other 2 sides are completely private.

I did put the blinds and the curtains on one side only to start with - south, because of the hot sun, rather than for privacy - but the curtains were so pretty when they fluttered in the breeze that I put them on all three walls in the end. Ditto the blinds when the neighbour said he was enjoying our candle-lit suppers, lol.

Try wrapping the curtains just beyond each corner for a more finished look.

Do all the sides, but on the sides you don't need privacy, gather them together and just leave as panels. Depends on budget though...those drapes aren't usually cheap.

$4.99 for a pair of polyester panels:

http://www.ikea.com/us/en/catalog/categories/departments/living_room/10700/?color=white&sorting=price

Or $19.99 for 100% cotton:

http://www.ikea.com/us/en/catalog/products/10111984/

Instead of pulling them back, try rolling the bottom of each panel into a love knot. It looks quite nice sometimes.

any more thoughts on curtains on one side only? The panels from Ballard are around $85 and I would probably need 4 on one side (space is 18 feet square). Also would two rods together look OK or should I look for one long rod?

I think you'll have trouble finding a rod long enough, at least at a good price. But if you can place two rods together at a bracket location, without finials where they meet, that might work.

I'd start with just the one wall, which I personally think will work fine, and then add others if needed.