Beast Strike is one of the best options available
Beast Strike is a feat from Dragon vol. 355 allows you to basically combine your unarmed strikes and claw (or slam) attacks, adding your claw damage on top of your unarmed strike damage. The feat is fairly unclear—we have a number of questions about how it actually works—but no matter how you answer those questions, it’s really good for this.
The reason is because normally, natural weapons like claws get used once, period. You cannot attack with that claw again; want more claw attacks? Get more claws. That conflicts rather heavily with the notion of flurrying with claws. Since in this case, you are making unarmed strikes, that just happen to get a damage bonus based on your claws, you avoid that problem entirely.
Rapidstrike and Improved Rapidstrike might be alternatives
These feats are in Draconomicon, and allow you to attack twice, and then thrice, with a pair of claws, rather than the once each you would normally get. This gives you something flurry-like, but it doesn’t actually combine neatly with flurry of blows. Also requires that you be an aberration, dragon, elemental, magical beast, or plant, so that’s a limitation (of these, there are playable, LA +0 options for aberration and dragon).
Ultimately, these are really costly and not a great solution. Beast Strike works much better.
For class, psychic warrior is almost-certainly your best bet for Wisdom
There are two classes that really excel at natural weapons in D&D 3.5e: the psychic warrior, and the totemist. Both are quite good, and both work, but I like the psychic warrior better for you because you want to be monk-like, and the psychic warrior runs on Wisdom. On top of that, you can take the Tashalatora feat from Secrets of Sarlona to get monk-like unarmed strikes, unarmored AC bonus, and flurry of blows—effectively, in two feats, you get everything good about the monk class added on to your psychic warrior levels.
That leads to a very-simple build of simply being (aiming for) a 20th-level psychic warrior, taking Monastic Training (psychic warrior) and Tashalatora at 2nd level (Tashalatora is a psionic feat you can take as a psychic warrior bonus feat; the only reason you don’t take it at 1st is because of the skill rank requirements), and then taking Beast Strike at 8th. Focus on powers like bite of the wolf and claws of the beast, along with mainstays like hustle, lion’s charge, and vigor.
But this has basically nothing to do with being a half-orc
Half-orc is a really weak race; it gets a net −2 ability score modifier, unlike every other race, and otherwise all it gets is darkvision, which is hardly unique. There is no psionic half-orc that I could find, no half-orc-specific feats or class features that grant extra natural attacks, basically, nothing.
A desert half-orc at least has a net 0 ability score modifier, so maybe that’s something worth considering. Run is a poor feat, but hey, it’s free.
Another option is the frostblood half-orcs from Dragon Magic, which are dragonblooded (opening up a number of feats, though only Races of the Dragon’s Dragon Tail is particularly good for you) and get Endurance as a bonus feat. They also have resistance to cold 10, but vulnerability to fire, which is a bad trade since fire tends to be more common and 50% extra damage will quickly be more than 10.
Really, though, there just aren’t a lot of options. Wizards of the Coast never gave half-orcs much love, not in Player’s Handbook and not in any supplement. You’re probably best off, if you really want to play a half-orc, to just play one, accept what it is, and focus on the rest of the character. There just isn’t much of any way to really leverage the half-orc race into something more.
If you can see your way to a non-Wisdom-based approach, though...
Usually, this is where I’d be recommending a full-blooded orc (especially a water orc) over a half-orc—they’re generally far better—but since you want Wisdom that seems like a less-good option here.
But, for the sake of argument, you could go with Constitution rather than Wisdom. Constitution’s connection to Concentration means it’s not totally unrelated here, and there are enough good options for it. And it’s not as if focusing on Constitution was ever a bad thing, from a survival perspective.
Constitution instead of Wisdom means (water) orc becomes a much better choice. It also means that desert half-orc does more for you than it would otherwise. I still prefer the water orc, but either works.
If you wanted to go that route, I’d suggest going for totemist, from Magic of Incarnum, instead of psychic warrior, and I’d say you really have to consider a barbarian dip because rage and pounce are so good for a totemist. You could, in my opinion anyway, easily reflavor rage as a kind of “zen focus.” You could then go for fist of the forest from Complete Champion for a monk-like AC bonus based in Constitution rather than Wisdom, as well as a class feature literally entitled “feral trance,” which grants you, among other things, a bite attack. A 1st-level barbarian/4th-level totemist/3rd-level fist of the forest would work decently well, for example. (If alignment concerns are an issue, note that there is a chaos monk available in Dragon vol. 335.)
I would still aim to take Beast Strike, since fist of the forest requires Improved Unarmed Strike. Actually, seeing as it requires that as well as Power Attack (and the pure-tax Great Fortitude; maybe ask your DM if you can use Cerulean Fortitude instead, at least that way you get a bonus essentia point), a single level of monk following the overwhelming attack style might be quite appropriate: get Improved Unarmed Strike and Power Attack in one level, plus Wis-to-AC that will stack with your Con-to-AC, and flurry of blows. That does mean you need to have some Wisdom, but even if you start with Wisdom 10, you can consider getting items that enhance it later in the game.
Ends up looking something like this:
||AC bonus, flurry of blows, unarmed strike
||Improved Unarmed Strike,B Power AttackB
||Totem chakra bind (+1 capacity)
||Fist of the Forest
||AC bonus, feral trance 1/day, unarmed damage
||Uncanny dodge, untamed strike
||Feral trance 2/day, scent
||Chakra binds (arms, brow, shoulders)
Of course, you can do more here.
You could drop the second two levels of fist of the forest—they don’t do very much. More meldshaping sooner is probably better.
You could consider cleric instead of barbarian, using Travel Devotion instead of pounce.
Again, if your DM lets you use Cerulean Fortitude instead of Great Fortitude for fist of the forest, starting totemist at 1st instead of 3rd so you can take it is worthwhile.
If you go for the frostblood half-orc, Dragon Tail is good, and you’ll definitely want Blazing Berserker from Sandstorm to negate your fire vulnerability (while raging)—at which point you probably want the Frozen Berserker feat from Frostburn to negate the cold vulnerability you get from Blazing Berserker (though your resistance to cold 10 will go a ways towards mitigating that).
You might even consider asking the DM if you can go with a desert frostblood half-orc—the largest deserts in the world, after all, are very cold—and then going with Weapon Finesse and ferocity instead of rage, just so you can ensure you have Blazing and Frozen Berserker up when you need them, and to improve your AC even further.
Steadfast Determination requires the rather-weak Endurance feat—which frostblood half-orc grants as a bonus feat! This is a fantastic feat, that prevents you from failing Fortitude saves on a natural 1, and allows you to use Constitution instead of Wisdom for Will saves.