Approach the problem from a writer's perspective:
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As an amateur author, DM and player my advice is stop trying to think up ways to "Make" your character dumb.  A lot of the other answers here focus on what I would consider superficiality and give only one or two highly specific behaviors to emulate "dumbness" as if it were an affliction, a curse of some sort.   This curse is akin to a pair of gloves of fumbling, that will present itself at opportune moments for comedic relief or trouble for the party.

Doing this to your Half-Ogre will not only render this character boring to play - but entirely mechanical, meaning you can set your character down - write out a rule sheet similar to computer code - and the DM himself can just reference your codified set of behaviors and know what your character is going to do.  Severely limiting your storytelling and development arc of your Noble (or not so Noble) half-ogre to mere hireling and up-plussed NPC.

Focus instead on framework of limitations and strengths to pull from.  Specific, consistent, behaviors are personality quirks best added *after* you figure out your basics.

I am going point out - not so subtly a major flaw in your character concept:

 - You are playing a Half-Ogre - **not** a retarded human.
 - Ogre's are a (presuming) "Darwinistic-ly" viable species that has proven successful at surviving despite "Low" intelligence.
 - Your characters instincts, common sense, and perspectives will be different than that of a full blooded human and that of a full blooded ogre.  Most likely a blending of the two.


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So lets set a framework of how your character can be "perceived" by mere human standards to be "dumb" without codifying a list of stereotypical behaviors that will pidgen hole your enjoyment at the table.

To start: Lets address the Ogre's general perspective on the world around it.   This is me theory crafting and talking out loud - but it's meant to be a brief attempt at creating what your character /might/ be like.   This is me freestyle writing off the cuff to give an idea of what I'm talkin about.

Ogre's are usually listed as solitary creatures.  Why?  Because they are the biggest and strongest around, and being the biggest, they need to eat lots to survive.  Its common sense to an Ogre that if a bunch of ogre's get together, they have to have larger and larger communal territories, meaning each ogre in that community will have to expend more and more energy to walk both to and from fertile hunting grounds.   Its a lot smarter to spread out and let each ogre have their own space.   And it makes a lot of sense that if your bigger and stronger, you get the better hunting ground.  I can prove my point by bashin in the weaker Ogre's head for good measure, or I better get clear or he might bash in my head.  Common sense.

Humans, with all that farming and cattle rearing - are wasting energy.  The heard know how to take care of themselves, so why spend all that time and energy cutting trees, scrapin dirt and building big fences, when you can just let the heard be, and walk on down there from time to time when you need a proper snack.  The only reason humans have to build such un-natural herds is cuz they don't spread out enough.   If humans wanna make big herds in my territory, I'll keep the human size down small enough so they don't threaten me.

Since I live alone, and everything I need is in my space, I don't need to "trade".   Because I don't need to trade, I don't need to learn advanced mathmatics.  I can still count to 20, 30, or even 40 on a good day, other than that, I can call it "lots" and be done with it.  

Along those lines, why should I spend energy and time thinkin up things that arn't real or goin to happen.  I can still think about what I need come winter time, or what might happen if I kick the human farm over, or make that hoard of orcs over there mad.  I can do cost-to-risk analysis's about how my behavior may affect the future.   But it tends to favor immediate actions.  If I attack that orc war party - I'm liable to be hunted.  If I see a magi - I probably should eat that magi first.  Am I bigger and stronger that that ogre?  Yes?  I'll smash his head in for bein in my territory.  If not, I'll make it happy and hope he leaves.

I don't like the human ideas of tradin.  If I'm bigger and stronger, and if it's in MY territory, I should just take it.  If they are the humies that made the thing, I'll take it and leave em be, cuz they might make more.  If I don't like them - THEN I'll take it, and eat them as a snack.

I would imagine Ogres have little reason to trade.  Other than appeasement gifts, or trying to carry favor with a potential mate - its either his stuff, or it isnt.   The abstract concept of "Coin for Labor" or the inherent properties (absudities) of gold doesn't make a whole lot of sense to a common ogre.   It has value cuz someone else says its valuable (A specific person or tribe of people).   To me something has value if it has immediate use or is something I KNOW will solve a problem I've seen in the past pop up.

Since the ideas of farming and mechantile trade are not part of my species culture, our ability to do math is limited, but not non existant.   I still need to be able to count and realize that 40 orcs are killable, 50 are not.

I rely more on my experience when planning for the future than anything "imaginative".  I still learn, I can still remember, but I place more emphasis on usefull things that represent actions.   If I've seen a river dam break and wash out a village, I can be clever and wash out another village that needs be removed if I see a similar situation - saving me energy.


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I can go on for hours playing around with this idea, but it gives you an idea of where I am going with it.   We have a character concept of a huge ogre that is intent on conserving energy and preserving itself and its assets in order to survive.   

He favors physical, tactile thinking, strategies and planning.  He learns from past experiences and think humans group up too much and waste too much energy on things that may not ever happen.   

Viewed from an outside perspective - he could be viewed as dumb and slow.  Not having a natural ability to count coin very well, or seemingly slow to react to something.  But in reality - he doesn't want to buy that bauble from the merchant, and his "slow to react" is actually him waiting to see how the initial conflict pans out before commiting his energy to the engagement.   He relies on his natural strength and simple - permanent solutions to his problems, rather than convoluted human schemes.

THIS is the point where you add character quirks:  Like him keeping a destrider (war horse) as a puppy.   If you add in many of the other suggestions - all your doing is boxing yourself into a corner.