Strongest Ninja?

I dig Edge and Yuffie, but really they're more useful as Thief-type characters. Their Ninja-type abilities really aren't all that exciting. Ninjutsu is unique and provides a rare MT elemental attack in FF4 (the water one), but apart from that, he's not bringing much to the team besides speed. Yuffie is similarly speedy and her long-range weapon stands out a bit in FF7 due to how important it is to be in the back row in that game, but apart from that, she's just as generic as the other FF7 PCs (though she -does- start with the Throw materia, so that's in her favor).

The original Ninja has an argument for being awesome, since he's a speed demon and gets great equips... but really, nothing in FF1 can stand out due to the brokenness of Fighter/Knight.

Really, it's got to be Shadow. Throw damage is consistently good for taking out bosses throughout the game. If you're stingy with thrown weapons, then Inviz Edge and Shadow Edge are great for laughing off physical-based enemies. Shadow has gamebest evade, not to mention the innate Interceptor block and counter. Top it off with being able to Steal like Edge and Yuffie and you've really got the complete package.

No comment on the TAY Ninjas, but I hear that they are all universally inferior to Edge.

My list is Shadow > FF3 Ninja > FF1 Ninja > Edge > Yuffie

While it may seem like I'm biased towards FF6, I'm really being objective here. It just happens that Shadow is one of the more broken FF6 characters.
If it had been a Thieves poll, you can bet Locke would have nearly bottomed out the list (Not that I don't like him, he's just not very strong gameplay-wise).