Haiji Mibu is a bouncer, and it shows. He's crazy powerful and surprisingly quick, and has some good combos. I play a little bit of everyone, but Haiji is my main.
Left-Handed Baby 236+p
Haiji leaps forward and delivers a punch to the gut. The button pressed determines the distance. Used in most combos without meter, and you can follow up with an OTG 3+HK. If you get your opponent in the corner, doing this over and over can piss your opponent off, because it briefly guard crushes when it connects.
Massacre Trumpet 214+p
Haiji twists back (can charge the twist) and flies forward with a deadly punch. Haiji has near-unlimited super armor when he's twisted back,so you can use this to eat up projectiles and counter, and it can make a good anti-air in a pinch. Horribly unsafe on block. Charging LP all the way doesn't do much, but a fully charged HP is unblockable and does 80% damage (don't expect to hit anyone with it though). This is also why Haiji vs. Haiji matches are fun as hell to watch: some crazy things can happen with this move.
White Sigh 623+P
Haiji's anti-air. Great damage, but kinda slow and can get killed if the jump in is deep enough. Remember, though: if you trade this with almost anything, the damage will be greatly in your favour. The move has a really screwy hitbox, I've seen players get hit from behind with it. This is also Haiji's all-purpose meaty attack. It's got a huge amount of active frames and decptive priority. On counter hit, it will pop the opponent into the air and can be comboed after. You can also get the same effect if you hit the opponent from really high, about 1/2 screen up.
Iron Moon 236+K
Haiji leaps forward with a kick. Much better range than LHB, and safe if you hit from far enough. Makes a decent poke, but not too many other uses.
A Subway Train Called "Despair" 236236+HP
This super takes a long time to come out (somewhere between Alex's stun gun headbutt and Iori's one-for-the-road blast), but does gobs and gobs of damage. The damage, however, is also dependant on positioning. The perfect position is right above Haiji and ever-so-slightly in the air; this should give 6-8 hits, and around 80% damage. Can be combo'd into, but only from certain attacks.
Sunglasses of a Dead God 2141236+HK
A lot quicker than his other super, but short range. Fair damage, but you can combo after it.
Bread and Butter Combos
j.HK, LK, HK, HP, 236+HP, 3+HK
j.HK, LK, HK, HP, 2141236+HK, wait,623+P, 236+K or (in corner) 236236+HP
Almost all of Haiji's specials instantly depelete the guard guage. For example, doing 236+P's one after another can be very annoying and surprisingly effective. Mix things up, and be quick about it. i.e. 236+LP, 236+HP, 3+HK, 623+P. You can easily overwhelm someone if you've got a basic understanding of his specials.