You're assigning a material in Blender. Odyssey doesn't use materials (except for walkmeshes), it uses direct texture assignment. Select the mesh, go to the Object tab, and in the KOTOR sub-panel look for the "Main Texture" field. Put the texture name in there, like so (vanilla example):
You don't appear to have an icon, which is why KSE is freaking out and it's blank in-game. Icons have to follow a strict naming pattern defined by the item type and referencing the variation number. In this case, your icon needs to be named iw_shortswrd_004. I would suggest using TGA for icons just to stop KSE's errors. Also don't make your icon bigger than 256x256, because KSE doesn't scale them.
Speaking of variation numbers, you're best to use a higher random number beyond the vanilla range. Less chance of a clash with other mods that way. The available range goes up to 256, so I'd use something like, I dunno, 139.