Java 3D can 'deal with objects' from other packages, but it depends what exactly you mean by 'deal with' : you can export geometry from 3DS/Maya into a form for which someone has written a Java 3D importer; with no theoretical limits whatsoever. Of course, practically, there aren't many importers. When I used J3D, I could just about get OBJ & 3DS files to display.. =D.
You would use code/script generally to 'move objects about', handle interactivity, and maybe for creating best-specified-as-procedural objects and effects, rather than actually writing every command to draw every vertex. It's usually obvious for any given object: if you want a tree, make it in a modelling package and export/import. if you want, for eg, a road for a racetrack, you might be better of generating it in code ( since you have more control/flexibility, and you can write code to make an object 'follow the road' or even true real-time collision detection [depending on level of interaction desired] much more easily if you already have 'the road' in a mathematical form ), but, it really depends.
Macromedia Director/ Shockwave is quite nice for 3D-in-a-browser. VRML has been re-incarnated as 'X3D' which, from some experience, is not the easiest technology to work with. I've never heard of Cult3D, and that's kind of an important factor if you're targetting browsers - in this day-and-age people aren't as happy to download new + unknown plugins as they used to be.
