I can't speak to the tengu sword (Looks like a bad, bent naganata), but the "ninja" sword is a modern fiction. There is no credible historical evidence of such swords in Japan. They are basically a modern Hollywood invention - pure fiction. I suspect the same for the tengu sword.
Rich S
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Richard Stein, PhD
"Old Puukkophile"
Japanese Sword Guide
http://home.earthlink.net/~steinrl/nihonto.htm
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