Does anyone know of an application that will treat various STL's as solid pieces?

Does anyone know of an application that will treat various STL’s as solid pieces? I don’t want to mesh them so much as see if they fit together like a puzzle. Thanks!

Sketchup maybe?

Solidworks (and many other CAD tools) can import stl files as solids if they’re not overly complex. You could then align the parts and use the combine bodies with the common option to find intersecting areas.
Blender also supports importing stl files and these kind of boolean operations.