Q:

How effective would wooden scale armor be in a medieval setting? 

In the western highlands live the warlike Oelha tribes.  The Oelha are infamous raiders left over from one of the hordes that ravaged the land generations ago.  Oelha frequently steal cattle and attack outlying villages of the neighboring kingdoms or other clans.  
While being warlike and vicious the Oelha are also fine craftsmen and metal workers their lands are poor in metal.  This means that most of the metals Oelha have go straight into the nobility and straight into swords. 
The Oelha need some sort of armor to be able to successfully raid further into their neighbors territory since they would come into contact with better arms and armor the further they travel.  The Oelha's solution was to make armor out of the trees that surround their homes. 
What I'm wondering is: would wooden armor cut into scales and sewn together be effective armor?  Would wood be able to hold up against weapons common place in the Medieval High Period?   Ex: long swords, long bow, pole axe, etc
Note: they have access to lots of oak trees

A:

So, wooden armour did exist in a few places where suitable metal for making arms and armour did not exist.  In similar places you might also find bone armour.  Here's an example of some aleutian wooden armour:

Here's a Haida armour suit, with wooden helmet (though they cheated and used leather over the wooden breastplate... may just be decorative, but I'm unsure on that).  The Haida had access to some metal (like copper) but nothing particularly useful for weapons or armour. 

The critical thing there is that metal weapons did not exist either.  The amount of wood required to usefully defend the wearer against metal weapons is just too bulky and too heavy.  It isn't impossible, obviously... people used wooden shields after all, but shields let you use a much smaller chunk of tree that isn't nearly so inconvenient, and is also easier to make so you can bring spares with you. 

Oelha frequently steal cattle

Then clearly they will be using leather and boiled leather armour, which is known to work and be staightfoward to make, and would use material that they would already have access to. 
That's not to say you couldn't use a hybrid design if it better fit your theme... here's a hybrid wood and leather outfit from siberia:

These things (as well as having the interesting winged design, overgrown pauldrons that were used like sewn-on shields) could be made from leather, bone, baleen or whatever other tough stuff you might be able to get your hands on.  It worked for the Yupik and Chukcki, because they lived in cold places and used arrows tipped with stone or bone.  As soon as they could get their hands on metal, they used that instead. 

A:

I don't have any evidence backing me up here, but I imagine it would be terrible against a well armed army.  That doesn't mean it doesn't have uses.  Similar to samurai who had paper plated armor, it would be useful against lightly equip soldiers, small militias or armed peasants. 
But once you get into the heavy metal armor, shield walls with pole arms poking through and above, and arrows raining down on you, its not much of a battle.  The formations used in the battle are going to make it incredibly hard for your soldiers to compete with. 
As a note, I doubt wooden armor would be 100% necessary.  A soldiers behind a tall shield doesn't need the best armor, nor does someone holding a long spear.  And as long as you can hit your enemy before they hit you, you don't need to worry too much.  Its a fairly fun concept in games.  You don't need armor if you never get hit.  
So as this is your world, your story, you could simply make your Oelha very skilled warriors who engage in small skirmishes, rather than in large battles.  Make them take advantage of the land and the terrain.  Woodlands to stop cavalry and obscure the vision of archers.  Mud and wet ground to bog down heavily armored soldiers.  
Wooden armor can be made to work.  It is better than nothing, but it won't hold much against a metal weapon designed to fight soldiers in metal. 

A:

Go Go Ghengiz Kahn. 
Ok, so you have a metal poor country.   That's ok, you can make up for a lack of metal with other things.   Mobility and ranged weapons are what comes to my mind.   It's a classic case of if you don't like the Answer, Change the question.   On perhaps, if you don't like the probably outcome of the battle plan, make a different plan. 
The OP mentions access to lots of Oak.   Fantastic, it's not the pinnacle of bow making materials but it will serve and it can make excellent arrows.   drop some other excellent bow wood trees in the area like Yew or Hedge.   So your people are going to be Archers.  
 The qualities of being an archer is going to have a huge impact on your armor design anyway. 
Next, you mention that they are raiders.   Now they could be on foot, or you could have them on horseback.   Either way, you don't want them to be over encumbered.   Boiled leather would do for most.   For those that are more likely to be in combat time after time a wooden scale mail might work.   It would be better than nothing. 
Here is how you could do it.   Take each scale and fashion it out of oak.   Then wind silk around it, mostly across the grain to help prevent splits, or to at least keep the damaged scale mostly functional if it does split.   Silk has the highest fiber strength I can think of for the weight.  Then attach the scales to the boiled leather in whatever pattern is effective and that moves with the archer. 
The fact that this kind of armor may not hold up against a direct attack from a great sword can be made immaterial by staying away from the great sword wielding jerks and shooting the horse out from under them and putting a ton of arrows in the joints of the armor and through the eye holes and such.   
If you make your archers mounted, yet another whole level of stuff opens up to you.   You can get lost in Wikipedia for hours studying the Mongols, the Huns, Scithians and on and on.   Just look at light cavalry tactics.   Incorporate these ideas to make them influence your armor design, not the other way around.