I tried setting mWorldProjection to the camera projection and mWorld to the transformation of the volumetric lines.
worldProjection = world * projection. Got that right?
To be crabby... Those aren't even volumetric lines. They're just fancy linear billboards with UV selection based on orientation... in an outrageously terrible implementation at that! You probably could write up proper volumetric lines if you're competent, which I recommend. When you integrate over the path through an OBB, I don't think you'll want to base it on sqrt() distance, which would be pretty (INSANELY) naive considering performance, but won't provide a fully realistic distribution anyway. I'll reply again if I can think of a good way to do this. Others can throw in their suggestions too if they want.
This might be helpful. I'm reading it myself and I'll try to put it into useful terms (appropriate for your needs).
One last additional remark
point sprites = billboards which are oriented about a point.
linear billboards = billboards which are oriented about a line.