I'm currently planning on making a 2D strategy game in Java.

Should I use Slick2D or LibGDX?

It depends on what you want to do. I have experience with libGdx and I assure you that as for 2d, you can do whatever you want.

About slick2d, i have no experience with it but... It's only for desktop? Libgdx is crossplatform (ios, android, html, desktop) so maybe it's what you're looking for...

As far as I know Slick is dead. LibGDX is an excellent framework though.

I am not sure about Slick2D.

I have tried LibGDX and it is an excellent framework. I highly recommend it, the community is very supportive too.