Is there a way to do serious social justice-related work or research while working on scientific research?
Can I use my skills as a scientist to meaningfully contribute to research that can have a meaningful impact on social justice?


Yes, you can.

In the USA, there is an entire union dedicated to this: the Union of Concerned Scientists.

Science is essential for the progress of humanity, and social justice is no exception.


The environmental sciences (including, but not limited to, climate science) have informed what is now a huge worldwide and successful green movement.  Where there is pollution or climate change, the poor are hit hardest, as they have least access to adaptive measures.  Therefore, action on environmental issues is closely linked to social justice.
Engineers develop low-cost energy solutions that help bring electricity and education to rural areas of poor countries that previously had no such access.  Or cheap ways to filter drinking water.
Educate members of activist networks.  Many networks of progressive action are lacking in access to science or engineering expertise.  If your knowledge matters to society, it matters to them.  Reach out to those groups.  They will welcome you!  


As an arbitrary starting point, you could consider the Craigslist Charitable list.  Are you a satellite engineer?  The space4peace group will welcome you (they will, too, if you are not).  Do you work in agricultural or plant sciences?  Surely some of the farm-related groups would love for you to come by.  Are you a nuclear (weapons) engineer?  Work on research on how to safely dismantle nuclear weapons.  Do you work in software engineering?  There's plenty of charitable programming to do, or to educate members of all kinds of groups how they can protect themselves from being spied upon.  Et cetera!  If you're into it, there's more direct action alternatives as well; a pipeline blockade may have get more attention if it includes a distinguished professor than if it consists entirely of "college dropouts".

You can combine this with an academic career (although depending on where you are and what you do, you may want to limit actions to stay out of jail).  Researchers at all levels from PhD students to professors are active in those groups.  It will be hard work, but it may well be that the volunteer time you spend with grassroots will motivate you, make your life more fulfilling, and ultimately even make your regular research work more productive.