Odile & Dokurod

Normals
5A - Fast, but short range and does not combo to anything under any circumstances. Pretty much worthless except maybe as a tick setup.
2A - Short and fast and chains to her target combo. But not a low, and 2B is generally better to use overall.

5B - Hits low and chains to 2B. A little slower than her other fast normals, but gives +1 on block so good for tick setups, and stronger than 2A so better for combos.
6B - Overhead. Fairly good range and startup for an overhead. Unsafe on block if not spaced right. Needs to be jump canceled on hit or block to make it useful.

5C - Very important normal for combos. Almost everything ends up chaining to this.
2C - Fast, but weak low hit. Can be useful as a poke to chain into Arabesque.

5D - Solid anti-air poke.
2D - Decent range sweep. Only jump cancels on hit. Disadvantage on block, but due to range, can be fairly safe.

j.C - Knocks down.
j.D - Cancels to Petite Pirouette. Good for resets.

Dash - Odile's dash acts somewhat like a teleport. You can use it to cross behind the other player, which can be very useful. It can still be jump canceled as normal. Has no invincibility.
Chains
2A -> 5A, 2B, 6B
2B -> 2A, 5B, 5C
5B -> 2B
Specials
236A/C - Entrelacé
Projectile. Nothing really fancy. Bad recovery time.
D version travels faster and does slightly more damage.
214A/C - Arabesque
Rapid hit attack. Steps forward and hits 4 times. Good for chipping and combos.
A version is faster and can combo off 2B. Can be canceled to Divertissement on the first hit, but this scales damage horribly.
C version steps farther forward, does more damage, and can be jump canceled on hit or block. Much, much better.
214B/D - Cabriole
Jumping "crossup" attack. This move seems to have been badly designed. It is supposed to crossup, but it rarely works correctly. Very, very unsafe on block. On hit, cancels to Petite Pirouette so good for combos.
B version is nearly worthless. Almost never crosses up.
D version can crossup but is harder to get a followup on. Can't crossup Deathbringer, Donvalve, or Ashley ever. Most characters it will only crossup if they are crouching or knocked down.
j.2B or j.2D - Petite Pirouette
Downward air dive, can only be done from a neutral or forward jump. Does not hit high. B version travels more forward, D version travels more downward and can crossup easily. Safe on block, but only +0 at best. Good for starting combos, crossing up, or covering distance.

Supers

214214P - Divertissement
Close range attack super. Not enough invincibility to be a useful reversal. Actually has longer range than it looks like. Kind of weak, but useful for a few combos.
j.236236K - Grand Pirouette
Super Drill. The higher on the screen it connects, the more hits you can get out of it, but the damage rapidly caps off. Extremely fast, can have as little as 1F of startup. Basic go-to super for combos.
Jump Cancel
Odile is unique in that she has the ability to jump cancel all of her ground normals. To do this, simply hold up after a normal hits or is blocked. The speed at which you can jump cancel depends entirely on the move, some are very fast (5B) and some are very slow (6B).

Ground Combos into Grand Pirouette

Because of the rapid startup of Grand Pirouette and Odile's ability to jump cancel, you can do many combos from ground normals into the super. You will generally need to Tiger Knee the super to get it to come out fast enough, by inputting 2362369, K.

Some example uses of this are:
2A 2B 5C 2362369K
5D 2362369K
6B 2362369K
And so on.

Option Select 2D

2D has the unique property of only being able to jump cancel on hit. This allows you to do a special Option Select with it. To do this, simply always input the combo:
2D 2362369K
On block or wiff, you will not be able to jump cancel and thus the super will not come out. On hit, the super will come out and combo. You can use this to your advantage when playing footsies to score extra guaranteed damage.

6B Jump Cancel

6B is unfortunately -6 on block, making it fairly unsafe, especially up close. However, jump canceling will allow you to leave the ground at about neutral advantage. This will allow you to avoid being thrown as a punish. It will probably not let you avoid getting jabbed, but you may be able to jump strait up, Gatchi, then Petite or Grand Pirouette as a punish.

The other use for 6B Jump Canceling is that, at close ranges on crouchers, it can combo into Grand Pirouette. The timing on this is difficult, but gives your overhead significantly more bite. Remember that on block, doing the super may also beat people attempting to punish you. But on block, the super will be wildly unsafe. Try to hit confirm the super whenever possible!

Dash Jump Cancel

Odile can cancel her dash into a jump like everyone else. However, due to the teleporting properties, this gives her some extra interesting options. After a knockdown (or any other time you can setup for it), you can dash, cross behind the enemy, jump cancel, and Petite Pirouette for an instant cross up attack. You can subtly change your timing to not crossup, or jump and do a late Pirouette for a double fakeout.

Keep in mind that do do the Petite Pirouette, you must be jumping neutral or forward, and when you jump cancel the dash, you will always be facing the enemy. So you must always jump Towards the enemy to get the drill to come out. Some examples:
668 (early) j.2D |> 2A/5B 2B 5C 214C ...
(No crossup)
669 (late) j.2D |> 2A/5B 2B 5C 214C ...
(Crossup)

668 (early) j.2D (late) |> 2B 214A
(Crossup)
669 (late) j.2D (late) |> 2B 214A
(Double Crossup)

Setups for this are few and far between unfortunately. Grand Pirouette at mid screen will score a knockdown, as will 2D, or j.C.
Heat Up

Double Jump

During Heat Up, Odile can double jump. This also lets her Jump Cancel any of her air normals, and her Petite Pirouettes.

Enhanced Specials

236A/C - Entrelacé
Hits twice, causing a lot more hit or guard stun.
214A/C - Arabesque
Hits 6 times.
214B/D - Cabriole
Can be canceled into Petite Pirouette even on block, making this much, much more safe and useful.
j.2B or j.2D - Petite Pirouette
Now hits 3 times and can be jump canceled. Frame advantage on block is still about the same though.
Combos

Basics

(Corner)
... 214C, jc j.C
(Knockdown)
(Corner)
... 214C, jc j.D, (j.2D)
(Reset)
(Corner)
... 214C, jc j.236236K
(Super)
Basic finishers for 214C in the corner.
(Mid)
... 214C, jc (j.2B)
(Chase)
Can't connect anything at mid screen, but you can use j.2B to follow them to the corner.
2A 2B 5C 214C ...
5B 2B 5C 214C ...
5B 2B 5C 214214P

(Far)
2B 214A
(Far)
2B 214A(1) 214214P

j.2D, 2A/5B 2B 5C 214C ...

214B/D, j.2D, 2A/5B 2B 5C 214C ...

6B, jc j.236236K
Only works vs crouching.
2D, jc j.236236K

AA 5D, jc j.C or j.236236K
Air to Air j.2D |> j.C or 214C or j.236236K

Gatchi Counter

5C 214C ...
[801/1531+]

(AA)
5D, jc j.C or j.236236K
[618/1300+]

High Gatchi Drive - Generic

(0 Mid)
5C jc j.D |> 214C
[785]
(1 Mid)
5C, 214C, jc j.236236K
[1147+]
Basic, easy combos. Works on anyone.
(0 Mid to Near Corner)
j.D |> 5C, 214C
[745]
(1 Mid to Near Corner)
j.D |> 214C, jc j.236236K
[1105]
(1 Deep Corner)
44 214C, jc j.236236K
[896]
Basics. Should work on anyone.

High Gatchi Drive - Character Specific

(0 Mid)
5C, 214C(1), 6 5C 214C
[835]
Coyori, Marco, Watson combo. Possible on Face but very hard.
(1 Mid)
5C, 214C(1), j.D |> 214C(1), jc j.236236K
[1199+]
Marco and Watson combo.
(0 Mid)
5C, 214C(1), 6 5C 214C(1), 214C
[862]
(1 Mid)
5C, 214C(1), 6 5C 214C(1), jc j.236236K
[1220+]
Urs combos.
(0/1 Mid)
5C, 214C(1)*2, j.D |> 214C(1)*2, 214C or j.236236K
[?/?]
Cedric and Ashley combos. Very height specific. More or less reps possible depending on height.
(0/1 Mid)
5C, 214C(1)*4, 5C 214C(1)*5, 214C or j.236236K
[?/?]
Freed combos. Very height specific. More or less reps possible depending on height.
(2 Mid)
Heat Up, 5C, 214C(1), jc j.D, jc j.2D |> 214C, jc j.236236K
[1510+]
Urs combo. May work on others. (?)

(0/1 Corner)
(Crossunder) 5D, jc j.2D, 214C or 214214P
[710/903+]
Hard. Only works on some characters. May be your best option against Deathbringer and Donvalve.
(2 Corner)
Heat Up, Late j.D |> 214C, jc j.D |> 214C, jc j.B, jc j.236236K
[1426]
Fairly easy, works on everyone if the spacing is right. When deep in the corner, you will need to jump back, but that does not work against Deathbringer or Donvalve at all, and may fail if too close to Face or Watson.
(0 Corner)
Late j.D |> 214C(1), jc j.D |> 214C(1), 214C
[813+]
(1 Corner)
Late j.D |> 214C(1), jc j.D |> 214C(1), jc j.236236K
[1164+]
(2 Corner)
Heat Up, Late j.D |> 214C(1), jc j.D |> 5C, 214C(1), 5C, 214C(1), jc j.B, jc j.236236K
[1560+]
Urs, Coyori, Cedric, Ashley, Freed combos. On Freed, delay the 214C after the 5C. Possible on Watson and Face, but very difficult.

Low Gatchi Drive

j.D j.2D |> 2B 5C 5D 214C, j.C or j.236236K
[1035/1507]
Works anywhere.

Heat Up

(Corner)
... 214C, jc j.2B(2), jc j.C
(Knockdown)
(Corner)
... 214C, jc j.2B(2), jc j.D (j.2D)
(Reset)
(Corner)
... 214C, jc j.2B(2), jc j.236236K
(Super)
Enhanced Heat Up finishers for 214C in the corner.
j.2B, jc j.2D |> 2A/5B 2B 5C 214C ...
214B/D j.2B/D, jc j.2D |> 2A/5B 2B 5C 214C ...