I've practised Shorin-Ryu Karate for years, and I've watched Kobudo demonstrations (my younger sister's a beginner with Kobudo too). Most of my knowledge comes from history and my observations from a couple Nunchaku demonstrations, so I'm sure that there are way more uses for it than I've told you.

Since Mikey uses two sets, I doubt that his fighting style would be nearly as defensive as using one (as I can't imagine how you can catch a sword with nunchaku and one hand) unless he was to use one nunchaku as a parry. If he used a nunchaku as a parry, he would have to be able to dodge at least one of Leo's hits, block another, and get into close combat. If he didn't, he'd be using full out offense and either knock away Leo's swords (which won't work if Leo is swinging them), or somehow avoid Leo's blades completely. Considering that Leo's a tactical genius, he probably wouldn't let Mikey get so close anyways. Nunchaku aren't that great in long ranged combat, so Leo would probably win either way.

But that doesn't mean that Mikey wouldn't win against say, Donatello or Raphael. In fact, I'd say that the turtles' weapons present some sort of Rock-Paper-Scissors scenario, except Donatello would constantly lose. Since they are all highly skilled warriors, I doubt that skill alone would enable Leonardo to take on say, Raph.

I'd already explained that Leo's would defeat Mikey, but he'd most likely lose to Raphael because the sai is incredibly useful for fighting longer ranged weapons. Assuming that Donny's bo staff is made of wood, it would be ineffective at blocking Leo's strikes.

Mikey's nunchaku would be ineffective against Donny if he were dual wielding. If he only uses one nunchaku, Donatello would only have to option of swinging at Mikey. Since Mikey's incredibly good at dodging, he would probably be able to beat Donatello. At the very least, he'd catch Donatello's bo and turn the fight into a match of strength. Interestingly, Mikey's dual nunchaku would probably let him beat Raph, considering the sai's offensive capabilities are short ranged and its defensive capabilities would at best protect Raph's wrists, but that sacrifices almost any chance of Raph winning. Because both are short range, Mikey could easily knock the sais out of Raph's hands.

Finally, Raph's got the edge over Donatello. If Donatello jabs, Raph can catch his bo. If he swings, Raph might be able to catch it, depending on the angle of the swing and the position of Raph's hand. Donatello's best bet would be to swing low, but that really leaves him open. If Raph catches the Bo, then Donatello needs to be able to overpower Raph and be quick enough to not get hit. While he could probably over power Raph (one hand vs two), I'm certain Raph would be able to hit him before he can respond.

Basically it comes down to who fights who first. Whoever fights Donatello first basically wins.