I suspect pesticide drift. 30 years ago I monitored drift from a canefield on the Big Island to Maui, confirmed by the U of H Extension. Pesticides cause leaves to resemble a distorted clenched hand.

Thanks for your suggestion. The sweet potatoes plant growing right underneath the papaya doesn't show any similar signs. I do have neighbors spraying for regular garden maintenance, but the plants are not very close and quite protected through hegdes. I do believe it's papaya ringspot virus. The images of "shoestring" leaves resemble mine. Is there a cure for it?

Not ruling out the pesticide drift though. My neighbors papaya is starting to show regular leaves. I will keep monitoring this closely.

I dont think ringspot looks like this.
you can check here though...

http://www.google.com/search?q=ring+spot+virus+papaya+leaf&hl=en&prmd=imvns&source=lnms&tbm=isch

i have read that boron deficiency will do this.
I have several papaya and when hurricane Isaac came through we got a LOT of rain for 2 weeks, it killed the smaller ones, the larger ones stopped flowering, and the leaves are deformed (kinda like this, but not as narrow).

I think the over-watering caused a boron deficiency,
which has corrected itself after it dried out a bit.

good luck, i luv papaya!