Differences from MK3
Recharge time added to single missile (also effects double missile)
Dash Punch recovery is longer.
Move List
Basic Moves
His LP run jab game is questionable because they hit slightly higher, allowing more chance for him to be uppercut or ducking LKed, his HPs hit high as well, and set up easy air juggle aaHPHP, JK, air throw for about 44%. His standing HK has good range and moderate height, excellent for anti airing half screen jumpers. His standing LK also has good range and positioning. His sweep is among the fastest in the game, abuse it. His ducking LK is a hair slower than some, but has good distance again. His RH has very limited range, but good height, useful for run under RH situations. His uppercut has a lot of height and range, but some characters can slip through it on cross ups, which is when you should for an anti cross up backbreaker. All of his air attacks are very good.
Special Moves
Gotcha Grab
F, F, LP (tap LP for multiple hits)
21% Damage
The Gotcha Grab is a sudden, fast move that is very safe to throw out randomly and the only real way to punish it consistently is to sweep when it comes out. There are obviously other ways to scout and punish it, so don't rely on it as a certain way to catch someone but it often does get people off guard and against blind rush down. With exact timing you can stick the Gotcha Grab in his 7 hit autocombo midscreen against Jax, and unmasked Sub-zero for a bit of extra damage that isn't really worth the effort, 51% with a punch starter, vs guaranteed 47% on everyone with a sweep instead, 47% with a LK on most characters, and 48% with a HK on a bunch. It is very useful for punisher combos, and in the corner off his autocombo, which can be extended significantly against many characters.
Missiles
Single: B, F, HP
Double: F, F, B, B, HP
10% Damage
Single and Double Missiles are great zoning moves because they take up a lot of space and move Jax backwards, so if someone jumps over one he is generally safe. In UMK3 they added charge time to the single missiles, and this also effects the doubles. If you fire a single missile, you have to wait a few seconds before you can fire a double, or another single, and vice versa. They were too broken in MK3 and decided to add this limitation to balance him. You can still use the double somewhat for zoning, or avoiding certain attacks with extra protection. You can mix the single missile with run jabs, and the double missile will hit teleporters from full screen as they go off screen.
Dashing Fist
F, F, HK
13% Damage
The Dashing Fist is a sudden move that can be useful to an extent, used as a wakeup particularly when getting up. Try to buffer the move without making your movements known as it is easily scoutable in that situation. In certain set ups, the Dash Fist will make Jax bounce off the opponent and move backwards, making him slightly safer than he would be normally. Do not over abuse it because it hits high and is easily duckable and punishable. It is possible to use this move to get you closer to an opponent as a method of dashing, but it is inadvisable, and you can also use it to extend corner combo juggles. It is also useful to get you out of certain situations and go back into zoning or sweeps. Sometimes you can use it as anti air and it generally makes Jax wind up right next to the opponent so you can go into run jabs, a combo, or sweep strategies as well. When used as anti air it can cause some glitch type scenarios where it will make Jax and his opponent push off eachother in opposite directions either facing towards or away and can create some opportunities for other tactics. There is no limit as to how many Dash Fists you can do in a juggle, nor is there a time limit inbetween so you can literally just frames a couple of them in a row in the corner as a humiliation juggle after his 7 hit combo.
Ground Pound
Hold LK for 3 seconds, release
12.5% Damage
The Ground Pound is another returning move from MKII, but it was given more start up frames to balance it, however it is still useful, and unblockable and only avoidable by jumping. It keeps your opponent on guard at all time and might put them in bad situations when they might not want to be in the air. Not many people actually use this move in UMK3 because of how much slower it is than the MKII version, but when used properly it becomes an annoying factor in a match, particularly if you time it to connect as soon as they hit the ground on a jump, this will force them to jump if they see it coming and they have to immediately decide whether they are close enough to counter the ground pound with a jump kick or a jump punch start to combo, straight up, or backwards. If you time and space it right, you will be on the advantage when they land on their second jump and be able to once again resume your now nasty, cheesey sweeping and back breakering techniques.
Backbreaker
Block (in air near opponent)
16% Damage
The Backbreaker is his golden move, because it is perhaps the most useful move in his arsenal, even though simplistic in usage and design. Air throws have tremendous zero frame priority in MK like regular throws in just about any game, including MK itself, but you can't avoid them in air or tech hit, and they generally do significant damage, in the mid-high teens and this is for one move that sets up tactical scenarios, generally accompanied by a JK before hand, increasing damage to about 30%. Whenever someone tries to cross up jump punch or jump kick you as you are sweeping them to a bitter end, anticipate it, and immediately, unhesitantly and committedly, jump forward, or straight up and tap block, and you will backbreaker them right back to the ground, then immediately return to the sweep fest. This tactic is also used with Kano and perhaps even more so. Even when you aren't sweeping, watch for any possible chance to get a backbreaker because it is also a psychological move. It makes people rethink what they are doing if you get them with it, 2, 3 or 4 times in a row because they think for some reason their cross up is going to work this time. Always remember to tap block a few times while you are in the air even if you aren't in a natural situation where you would instinctively backbreaker someone because chances are you'll hit it. Remember that Robot Smoke's radius for his air throw is very large, pretty much 360 degrees around him while Jax's has a bit less area to deal with.
Multislam
Tap HP during a throw
6% Damage per slam
The Multislam is simply a special throw, in which you perform a normal throw, and tap HP several times to get 3 more slams. There isn't much more to it other than you can go back into sweep tactics after it!
Finishing Moves
Fatality 1
U, U, D, DF, F, UF, U, BL (Next to) (Hold Block)
Jax's arms turn into big blades. Then he cuts his victim up into many pieces which then fall to the ground.
Fatality 2
RUN, BL, RUN, RUN, LK (Half Screen)
Jax grows very big very quickly. Then the screen moves to just show the victim. Then a big boot of Jax's smashes the victim.
Friendship
LK, RUN, RUN, LK (No Block in Winning Round) (Past Sweep)
Jax jumps rope. Very stupid.
Animality
Hold LP, F, F, D, F, Release LP (Mercy First) (Next to)
Jax turns into a gold lion and mauls his victim.
Babality
D, D, D, LK (No Block in Winning Round) (Past Sweep)
Mercy
Hold RUN, Wait 1 Second, D, D, Release RUN (Round 3) (Past Sweep)
Stage Fatal
D, F, D, LP (Next to)
The Basics
Strategy
As Jax
He's a sweeper, a zoner, a back breaker-er, and ground combo crusher. He's got a lot of options but he struggles against teleporters and other top tier characters. Take advantage of old tactics like standing HKs, ground pounds, sweeps, watch for cross ups and hit the back breakers, sweeps, keep away with missiles, sweeps, rush down with run jabs and the 7 hit combo but be careful on male ninjas and some other characters because often times the 7 hitter will whiff on the D HP (HK, HK, D HP) leaving Jax open for a free counter, in some cases disastersouly damaging because he is the easiest character to juggle, oh yeah and sweeps. Play as cheap as possible with him, perhaps even turtle or read other players, and play safely because he can be annoying to rush down due his range.
VS Jax
Combos
Basic Juggles: 
1. aaHP, Gotcha Grab 6 hits 27% (add an extra aaHP, but requires stepping forward a bit depending on the opponent) 
2. (as a punisher) aaHP,HP, JK, air throw 4 hits 44% 
3. Add a HK on Male Ninjas, Sub-zero, Jax, Stryker, (Robots, Sheeva require a small step forward), and a few other characters, for 39% instead of 33% on his 7 hitter, leaving off the last B HP, a standing LK works on a lot more characters, for 37%, and a sweep will work on everyone also for 37% and sets up tactics, you can do his Gotcha Grab with perfect timing on Jax and unmasked Sub-zero for a few more %. 
Basic Corner Combo - Juggles: 
punch starter, HK, HK, D HP, HP, BL, LP, B HP, with your choice of finish: 
1. HK - 50% 
2. RH - 51% 
3. gotcha grab 13 hits - 53% 
4. uppercut - 54% 
Advanced Corner Combo - Juggles 
punch starter, HK, HK, D HP, HP, BL, LP, B HP, with your choice of finish because certains combos work more faithfully on specific characters: 
1. RH, HK - 10 hits 59% 
2. JK, Backbreaker - 10 hits 59% 
2. aaHP, dash punch, HK - 11 hits 60% 
3. aaHP, dash punch, aaLP, gotcha 16 hits 65% (against Robots, Kung Lao, Jax, Sheeva...) 
4. JK, aaHP, dash punch, HK, 12 hits 68% 
Corner Juggle Punishers: 
1. aaHPHP, dash punch, HK 4 hits 40% 
2. aaHPHP, dash punch, aaLP, Gotcha Grab 9 hits 52% 
3. aaHP, JK, aaHP, dash punch, HK 5 hits 56% 
3. aaHPHP, dash punch, JK, backbreaker 5 hits 58% 
4. aaHP, JK, aaHP, dash punch, aaLP, Gotcha Grab 10 hits 68%


MK2

Combos
Auto Combos

1. HP, HP, HP, LP, B+HP 5 hits 28%, 33%, 35%

2. HK, LK, LK, HK, LK, B+HK 6 hits 28%, 37%, 39%

Advanced Juggles

1. (near corner) aaHPHP, JK, air wave, aaRH, R+HK 6 hits 78%

2. aaHPHP, aaHP, JK, air sonice wave 6 hits 46% (BP)

Special Moves
Energy Wave: F, DF, D, DB, B, HK

Air Energy Wave: F, DF, D, HK (in the air)

Backbreaker: Block (In Air) (Next to)

Gotcha Grab: F, F, LP (Tap LP for more hits)

Ground Slam: Hold LK for 3 Seconds, Release LK

Quad Throw: Throw and tap HP repeatedly

Finishers
Fatality 1 "Head Smash": Hold LP, F, F, F, Release (Next to)

Jax claps his opponent's head into pieces.

Friendship "Jax and his dolls": D, D, U, U, LK (Past Sweep)

Jax cuts out a row of paper dolls and holds them up.

Babality: D, U, D, U, LK (Past Sweep)

Brutality: HP, HP, BL, HK, LP, LP, HP, BL, HK, HK, HP (Next to)

Stage: U, U, D, LK (Next to)