I'm sorry. Your image link doesn't work. But, based on your description, it sounds to me like the fruit are infested with the larvae of the plum curculio, which is a very common and major pest of fruit. They cause what you describe - misshapen fruit, which in the case of stone fruits can ooze sap from the wound where the female laid the egg. Cut some open and see if there are white grubs inside eating the fruit and the forming seed. If it is the curculio, check out the numerous threads on here about controlling them. Sevin won't work at all, the PC is basically immune to it. Imidan is the chemical of choice, but the timing of the sprays is very, very precise.

kans: Your tree has peach leaf curl. Yes it infects nectarines also. You need to spray 2-3 times between leaf fall and bud swell in spring. Spraying after bud swell does no good because the leaves are already infected. Collect infected leaves and dispose of them in the trash. Here is a link that might be useful: peach leaf curl management

bellegrovegardener, Try this SITE

It might have something to do with all the rain. Mine did ther same thing. I got over 15" of rain in less than 3 weeks. All of my nectraines are spillting from all the rain.