"A kata may be regarded as an integration of offensive and defensive techniques, but it is more than that. One should try to understand the spirit of the master karateka who created the kata, for it has a life of its own and requires five or six years to be mastered."
- Hironori Ohtsuka, Wado-Ryu founder

Kata - "Formal movements"; in the context of Japanese martial arts, an "imaginary fight".

Bunkai - Principles and application of kata.

Kata:
Wado-Ryu kata tend to use the Okinawan names. Also listed are the Japanese names that Wado-Ryu shares with Shotokan karate. I have also listed various other kata I am aware of.

Kihon Kata Shodan / Nidan
Basic Forms 1 and 2

Pinan (Heian) series: Shodan, Nidan, Sandan, Yodan, and Godan
"Peaceful Mind" Numbers 1-5. Said to be created by Anko Itosu in 1905 or 1906, basing them on Kushanku, and a forgotten kata called Channan. There is some debate as to whether Kushanku was instead formulated from the Pinan series, however.

Kushanku (Kanku Dai)
"Sky Viewing". Said to be the most advanced of all Okinawan kata.

Bassai
"To Penetrate A Fortress". An Okinawan Tomari-te kata. It uses dynamic stances and hip rotation to find a way past attacks.

Wanshu
"Flying Swallow". A Tomari-te kata based on movements brought to Okinawa in 1683 by a Chinese envoy of the same name.

Naihanchi (Tekki Shodan)
"Holding your ground", "The Iron Horse", or "Battlefield". Named after naihanchi dachi, which the kata centers around. This kata was transmitted by Matsumura-sensei throughout Shuri and Tomari sometime before 1825.

Jion
"Temple Sounds" / "In the Jion-ji Shaolin Temple". A Tomari-te kata, it is named after the Jion-Je, a Buddhist temple. This is a strong kata practiced in Shotokan and Wado.

Jutte (Jitte)
"Ten Hands". It is said that anyone who masters this Tomari-te kata has the strength of 5 men. Sometimes practiced in Wado.

Chinto (Gankaku)
"Fighting to the East" / "Crane on a Rock". Taken to Shuri province in Okinawa by a Chinese sailor of the same name, Chinto is based mostly on White Crane Kung-Fu. Ohtsuka-sensei knew a variation of this kata.

Seishan (Hangetsu)
"13 Hands"/"Crescent Moon". Named after seishan dachi, it is based on movements brought from Fukien to Naha circa 1700. Ohtsuka-sensei also knew and taught this kata.

Rohai (Meikyo)
"Clear Mirror", "The Mirror of the Soul", or "White Heron". This Tomari-te kata is practiced in Wado.

Suparimpei (Pechurrin - Chinese name)
"108 Steps" (represents the 108 evil spirits of man). Developed from a Chinese form used in systems including Dragon Boxing and Tiger Boxing. Practiced in Wado.

Niseishi (Nijushiho)
Transmitted by Ankichi Aragaki, variations of this Shuri-te kata exist in Shotokan, Shito, and Wado.

Unsu
"Defense of a Cloud" or "Cloud Hand". This Tomari-te kata is practiced in Shotokan, Shito, and Wado.

Sei Shi
"24 Steps". A Shorin-ryu kata performed in 3 directions - the points of a triangle.

Seipai
Variations exist in Goju-ryu and Shito-ryu. It was influenced by White Crane Kung-Fu.

Annan
A Shito-ryu kata that primarily uses open hand techniques. It also has a Goju variation. Annan has great versatility and speed in its self defense techniques.

Useishi / Gojushiho Sho
"54 steps" number one. A Shotokan kata.

Gojushiho Dai
"54 steps" number two. A Shotokan kata.

Ji'in
Variations exist in Shotokan, Shito & Wado.

Nipaipo
A Shito kata with a Chinese flair.

Kihon Kumite Kata (Basic Sparring Forms):
The 1st 10 out of the original 36 are still practiced in many Wado dojo. These kata are two-person drills.
Ipponme / Nihonme / Sanbonme / Yohonme / Gohonme
Rokuhonme / Shichihonme / Hachibonme / Kyuhonme / Juhonme

Bunkai:
Kihon Kata Shodan
Basic awareness, stances, defenses, attack angles, economy of motion, & focus. High Blocks 2 & 3 may be used as strikes.

Kihon Kata Nidan
It teaches power generation through hip twisting and body torque as well as momentum.

Pinan Shodan
This kata helps movements become stable, efficient, and intimidating. The first technique, "c block", sets up for a redirection. Even the sword hand blocks can become attacks.

Pinan Nidan
This kata instructs further on timing, distance management, body shifting, consistency of stances, and redirection of attack. The first half may be interpreted in various ways. When practicing Pinan Nidan, imagine perceiving an opponent's intent and counter-attacking quickly.

Pinan Sandan
This kata teaches a continuous guard. It also helps become less predictable, and more efficient. The middle & low blocks in the beginning may be termed "continuous block", which may be interpreted in many ways. The turn after the spearhand strike, and follow-up with the outward tetsui, is twisting out of the opponent's grappling of your arm, and countering.
The use of the elbows in naihanchi dachi may be either strikes or strong blocks. This may be interpreted in many ways in close quarters. The last moves of the kata may be seen as elbowing to both the back and front, or breaking a rear grapple with an elbow to the opponent's abdomen and a hook to the face.

Pinan Yodan
Stepping into a back stance as you double block disrupts the opponent's movement, as you simultaneously block and counter. Blocking behind you immediately after the initial blocks cuts a sneak attack short. The low block, front snap kick, and elbow combination will block, stumble, and knock out an opponent. The sequence after the second elbow assists in learning how to follow through with attacks, and helps practice economy of motion.
The cross-block that begins the second half of the kata counters a grab attempt. Pulling the hand back as you kick may be
interpreted as trapping the opponent's arm under yours, and pulling him/her into a kick to the groin.

Pinan Godan
The high cross block sets up for an arm lock, tetsui, and finishing punch. The jump ends with a strike to a fallen opponent. The palm strikes followed by pulling motions represent attacking the groin and causing severe trauma to it.

Kushanku
The Pinan kata help one understand Kushanku, as there are many similarities. The ready phase of Kushanku clears the mind. The slow motions may often be used as blocks and/or attacks, but it is preferable to perform them slowly for breathing and focus. Practice consistency in stances, torque, and momentum in this kata. Kushanku provides endless insight, and help greatly in the study of other advanced kata.
In the second half, the sequence that ends with a punch to the ground represents blocking a kick, throwing the opponent, and knocking him/her out. The next sequence blocks and throws an opponent, then jumps over him/her to kick another, and follows through with a finishing strike. The last sequence is a takedown with a knockout blow.

Bassai
Bassai builds a stronger, more efficient defense. The first two middle blocks may be seen as a kick counter and takedown; the backfists near the end may also be used this way by performing scooping blocks to set up for the attacks. The crescent kick is a block to set up for the elbow strike. After the elbow is 3 sets of double strikes to counter a rear grapple attempt.

Wanshu
Wanshu, like Bassai, is technical and efficient, but is of a more aggressive nature. It is also a study in timing and follow-through. Stepping into side stance as you set up for a low block may be seen as body shifting to dodge an attack, as you move in to punch the opponent. The jump represents stomping on a downed opponent while preparing to block an attack from another.

Naihanchi
Naihanchi develops lower body strength. It also teaches one to settle all one's strength in the abdomen/center and draw from it. The methods employed in Naihanchi are best applied and interpreted in a narrow space.

Seipai
As an Okinawan kata, Seipai uses a small structure to reinforce mobility. Due to the Crane influence, Seipai is a study in entering and parrying. The first combination blocks and pulls a low attack, then knocks the attacker down. The rolling motion of the arms after the turn, low block, middle block, and mawashi uke combination represents a damaging arm lock. In a variation of Seipai, juji uke is performed just before the sweep. The last two strikes of the kata knock the opponent down, then out.

Gojushiho Sho
This kata is a study in close quarters techniques. The first sequence is a double wrist block, and counter attack. The sequences after the elbow strike represent a kick counter, nukite, and grapple counter. The last sequence represents blocking an attack to the midsection, blocking a grapple attempt, then counter attacking to the collar bones.

Annan
Annan contains many practical, efficient counter attack methods. It is also very useful in practicing breathing, focus, and fighting principles. Raising the knee and striking with the finger may represent blocking a kick, then hitting the vital point below the ear. Stepping into naihanchi dachi, extending the hands, and clinching them into fists will jam the opponent, and grab him/her to gain control for the side kick. The "ox jaw" wrist blocking sequence near the end blocks a middle punch, then knocking the shoulder out of joint.

Jion
Jion is very direct, yet powerful, stable, and technical. Its use of stances will greatly assist your footwork. Remember, the physical side of fighting is done from the ground up.
The first technique may be considered as a striking block, and its uses are numerous. Compare this to Pinan Sandan. The low block and middle block in back stance sequence sets up for a pulling block and punch counter. Performing low block in back stance, then a supported backfist in jigotsu dachi may represent blocking a low punch, then sweeping a kick.

Overview:
Aside from the dojo precepts, kata is traditionally Karate-do's primary tool for personal development. It is the textbook of Karate-do that is to be learned, understood, and applied. It is the tool by which Karate-do demonstrates fighting principles, but also creates unity in one's body, mind, and soul.
What may seem unnatural motions become second nature with training and practice. Kata assists in drilling good habits, and replacing bad ones. Once the techniques have been absorbed, patterns, principles, and body mechanics may be understood. The "art" of "martial art" is understanding these underlying ideas, that guide techniques and give them meaning. A technique is not just a strike or block, but also the factors necessary for the technique to work (timing, movement, and so forth). By practicing kata, and drilling "bunkai", you will learn to apply principles with no extra "clutter".
The fighting principles, when well applied, will work in many situations. Awareness and defensive principles help avoid, assess, or diffuse encounters. The search for unity means we should use lethal force as a last resort. The key is to move last, but hit first. In this way, there is no first strike in karate, but we meet force with a passive counter. Look for new ways to interpret kata - many secrets may be found…or created.
Mentally, kata teaches focus, and attention to all angles. One must cut through disclarity of mind to understand kata, and with this a growing process takes place. You will find bunkai where you did not before, as you imagine the problems the kata creators faced. This problem solving that kata teaches is invaluable. It balances the mind and grounds it to a reality that is still unpredictable, yet enriched by clearer understanding.
Physically, kata enforces proper use of body structure. It also strengthens the muscles through natural body weight exercises. Practiced vigorously, kata improves cardiovascular efficiency. Kata is therapeutic and empowering.
Spiritually, kata provides a path of self awareness. In practicing or even creating new kata, one builds resolve. In aiming for mastery, one builds patience. In either, one has to continually search in and outside of themselves, that one may learn how to apply the truths contained within kata.