A J-1 holder can definitely submit a I-140 petition based on NIW or EB1. As long as the person is qualified, it does not matter at all what non-immigrant status you are under, whether J, H, or otherwise. It's your qualifications that matter. However, two things to keep in mind as a J visa holder:
1- The most important is that, while you can submit your I-140 petition in either category (or both), you may not be able to submit an adjustment of status application (I-485) even if your priority date is current if you are subject to the two-year home residency requirement. You must either comply with the requirement or obtain a waiver before submitting your I-485. However, you can still submit the I-140 anytime.
2- Once you submit your I-140 petition, you are placing your J status in danger because, by submitting an immigrant petition, you are showing immigrant intent, which contradicts the purpose of the J status. First, you may not be able to extend your J status. Second, if your J-1 visa in your passport is expired, you are unlikely to be able to obtain a new visa at a consulate abroad even if your DS-2019 is valid. Third, if you travel and you do have a valid J visa, you could still be denied reentry when you arrive in the US. Therefore, if you decide to go that route, make sure you will have enough time on your existing DS-2019 to obtain a waiver of the home residency requirement AND make sure you have no plans to travel until you get the waiver so you can submit your I-485 and obtain an Advance Parole document.