I was on an F-1 visa, my wife is American and I got my GC through EB2-National Interest Waiver program while I was a in my 4th year as a PhD student. For NIW, you'll need two applications I-140 and I-485. Once I-140 is approved, I-485 will adjust your status from whatever visa you are at now to that of a permanent citizen.
My friend was on J-1 (he is single), he applied for I-140 (NIW), but even if he got approved, he will still will need to go back home for 2 years then apply for I-485 (adjustment of status) after that to get his GC.
However, in your case since your wife is American, you can get a waiver and out-rule the 2 years rule. You will need to have a good lawyer and spend some time at the court. But again, since she is American, she can go back home with you (if possible). Keep in mind that count for citizenship starts ONCE you get a GC (and not when you got married).
For instance, I got married in 2013, but in 2015 I applied for NIW and got my GC within 10 months. It would have been cheaper, faster and easier to apply for GC through marriage [in my case since I was on a F-1!]. But, to be honest, my credentials are extremely good and I figured getting GC through NIW would feel like an accomplishment and looks much better in my resume.