OK, sorry for giving you the runaround - I've just been really busy with schoolwork lately, and I've just been suggesting things you can try because I haven't had time to look at the .x file very much. I guess the exporter is just screwing up somehow, and I can see where the faces are defined as groups of vertices (it's the section where you have a bunch of numbers in groups of 3 all in order)... I wonder if the faces are being exported inside-out for some reason? I know this exporter used to work, with Wings version 0.98.35... I wonder if something in Wings changed in version 0.98.36 that broke it? You should be able to download old versions of Wings from the sourceforge site; maybe try exporting it from 0.98.35? (You will have to copy the wpc_x.beam file over from 0.98.36 though, since it wasn't included in that version - it should be in the wings/plugins/import_export folder...)
Again, sorry this isn't working for you...
edit: Aha, I think I found it... your model does not have any material assigned to it! Try assigning one of your images that you have in the .wings file as a texture (or just convert vertex colors to materials), and then export... Looking at the wings forums I found one of my old posts in which I explained that objects without a material assigned won't export properly, and I seem to have forgotten about it! (Well, I am at school and I don't have wings installed here so maybe your model DOES have a material and I just couldn't tell because it was all gray like the default vertex color, but if it doesn't, give it a shot!
)