In regards to how they were used, I think there is no doubt that conventional katars are well documented as being nasty punching (stabbing) weapons. I've thrust (punched) mine into some thick foam before, just for fun, and the "wound channel" that was generated was quite impressive. Just a theory, but curved katars might have been created to capitalize on soldiers that felt more comfortable using the standard style of swinging a weapon in India; keeping the wrist stiff and slashing at an opponent instead of punching/stabbing them. No doubt a curved katar - or even a straight katar - functions (cuts) just like a really small pata. A curved katar might = a better cutting weapon, but any difference in that regard clearly wasn't important enough to create a large amount of them. It's possible that being so out of place in regular society made them not important enough to be named. Though I don't doubt that if you asked an Indian to give a name for a curved katar back in the day they would have just respond with (x) jamdadu/jamdhar. This given the whole thing that the "pattani" of pattani jamdadu - a long straight katar - comes from the (old?) root word "patta", a word used to describe a long, straight blade of grass (I believe Elgood notes this in Hindu Arms&Ritual). I think one of us really just needs to learn Hindi and then we can come up with our own specialized terms for these katars
.
Regarding the actually unusual styles of katar, this is rather puzzling. Personally, I think having a multi-pointed katar (not one with multiple blades, just points cut from a single blade) is actually somewhat viable. Of course the points spread out the force, but assuming one can punch well with a regular katar, the force generated should still be sufficient enough to embed all the points into a target. To get a bit graphic, in regards to getting stuck on things (bone), a regular punch to the chest with a katar would
maybe punch through bone, but more likely than not be redirected between the ribs. Depending on the angle and force applied, the widening of the blade could also push apart/cut into/crack nearby ribs, causing further damage. In regards to a katar with multiple points, just imagine the aforementioned, but the blade is wider, and (with a heavy maybe on this one)
might be a bit more massive so as to do more percussive/bone-messing-up damage. I suppose realistically, my "thesis" here is just that more points should equal a more graphic, gory wound.
Multiple blades should, in theory, work the same, but with them all being so thin I can see them also being relatively easily damaged.
As a side note on the bifurcated Rajput-style katar (an example being one in Jens' catalouge, pg 134-135), I could see this one as either being an early tourist attraction kind of invention, or, again, a valid type (the construction of the blade - which splits into two only after the forte - seems relatively solid) that could create a more violent wound if used correctly.
"Scissor katars", IMO, are a total joke. Regardless of parrying possibilities, they seem to be so flimsily constructed that it seems to me a hit anywhere on the weapon would disable it's silly "amazing expanding blade action!" It also seems to me that if you want to ever actually use (punch with) a katar, you have to first squeeze the crossbars to adequately hold onto the thing, meaning the blades would always be open; ready to dent, chip, or break off as soon they get hit with an actual weapon.