Nuki-waza makes the opponent's strike empty in the air. It requires a lot of skills to make that happen.
Nuki-wazas include men-nuki-do, men-nuki-men, men-nuki-kote, kote-nuki-kote, and kote-nuki-do. The most common is men-nuki-do and it's usually called nuki-do. Other nuki-wazas are relatively more difficult to implement. Hence, the explanation of nuki-waza below is devoted entirely to nuki-do.
The most difficult part of this waza is to make the opponent's strike empty. If you accomplish that, 90% of waza has already been done.
To successfuly do a nuki, there are a few points to keep in mind;
After you succeed in a nuki, you should quickly strike the opponent's do. To do so, be conscious of the path of your shinai. It has to be the minimum distance possible. You should not strike a do as if you drew a circle with your kensen. Try to cut linearly. Bring the shinai toward your left shoulder quickly and cut the do diagonally. The path of your shinai should almost be linear. If your shinai draws a circle, your do strike is likely to be too slow to seize the moment.
Try to strike a do with your right hand. Left hand should not be holding the shinai tightly but only softly. This allows the quick turn-around of your hands for a fast and firm do strike.
Again, the timing is cruicial. Try to strike when you are passing by the opponent under the left armpit. Do not be afraid. Step boldly into his armpit and strike as you are walking past him.
Kaeshi-waza has two parts to it; you block the opponent's attack and then counter-attack right afterwards.
In this waza, it's critical to do the transition correct from one move to the other. Particularly,
Baseball analogy may be useful here. Think of a situation when an infielder catches a ground ball and throws it to the first base. When he is about to catch the ball, he moves his glove forward a little and wait for the ball. Then, the instant he catches the ball, he pulls his glove toward him a bit to partially kill the speed of it. Then, as he catches the ball, he is getting ready to throw it by grabbing the ball in the glove with the right hand and pulling. All he needs to do is to use the momentum of pulling backward and to effectively rotating the shoulder to throw the ball.
This example shows how the two actions are combined smoothly and efficiently. By this, an infielder can catch and throw very fast and precise. Kendo is no exception.
Think about men-kaeshi-do. The opponent comes to your men. You block his(her) men strike with your shinai and hit his(her) do. When blocking, you should first raise your arms as in suriage waza. Then, as soon as the shinais are met, move your shinai to your left shoulder and change the course of the opponent's strike. His shinai is off of your men now. As soon as you do that, turn your wrists around and quickly strike his do.
To give a strength to the strike, try to strike the do with your left hip. Twisting your left hip inward (clockwise) as you strike the do gives you the extra edge (sa-e) to your strike. As always in do strikes, the quick turnaround of the right wrist is crucial as well.
There are a few "don'ts" in this waza:
Suriage has two parts to it. "Suri" means to "rub" and "Age" means "up". As the opponent comes to strike you, you counter his shinai by rubbing it up with your own. Once you did suriage, all you need to do is to drop your shinai down to strike the opponent. The following is the description of men-suriage-men, which is the most common suriage waza.
It's critical what angle your shinai touches the opponent's. As his shinai comes down to your men, your shinai should face just a little bit outward to your right and counter his shinai. Of four pieces of bamboo that make up a shinai, you rub the opponent's shinai with the left piece. Also, the speed of your shinai going up should accord with that of opponent's strike going down so that you can effectively do a suriage up in the air.
Suriage-waza needs to be conducted very fast. Consequently, you hardly use the shoulders but your elbows and wrists. You should do a suriage with your right pinky and strike with your right pinky as well. As you raise your arms, you should twist your right wrist clockwise and rub up the shinai.
Don't step or lean backward when you do a suriage. Rather, you almost step or lean forward to counter the attack, or stand on tiptoe. As soon as you did a suriage, you should strike immediately. Otherwise, the distance gets too close and the strike becomes too deep. Also, you may want to step to your right as the opponent tries to go straight toward you.
There are "omote" suriage waza and "ura" suriage waza. The difference is that "omote" rubs the shinai with the left bamboo piece where ura rubs with the right piece.
The way to use your wrists and move your body is a mirror image of omote suriage. A lot of people do not correctly use their wrists, though. They tend to bend the right wrist outward to block the opponent's strike. It is a bad habit you do not want to pick up. The correct way is to twist the wrist counter-clockwise without bending it so that the paw of your right hand faces to the floor. Similarly to the omote suriage, you should do a suriage and strike with your right pinky.
The most popular and practical ura suriage waza is kote suriage men. You see a lot of this waza in matches among high school and college players. Hence, the explanation that follows is about kote suriage men
Uchiotoshi waza is the waza where you strike down the opponent's shinai just before it hits your men and you strike his men immediately afterwards. In other words, you strike down the opponent's shinai in the middle of striking his men.
To successfully execute this waza, your aggressive state of mind is critical. You should not be intimidated by the opponent's strike. Rather, you counter that with more aggressive attitude by stepping forward and almost riding on the opponents' body (noru-kimochi).
The timing is also critical. You should keep looking at the opponent's shinai and do a uchiotoshi above your head as forward as you can. You men strike should accord with his.
There are several wazas you can do with uchiotoshi and the way you move your body is different in each of them. In men-uchiotoshi-men and kote-uchiotoshi-men, you should go forward. In do-uchiotoshi-men, you should step backward because when you uchiotoshi do, you are already too close to the opponent.