Not quite sure what you're asking, but if you are asking if an Ogre Magi can change shape to look like an Orc, the answer is "Yes!". Is that a great idea for messing with your player? "Yes!" ()
Would an Ogre Magi's children ever be half-orcs(/half-humans)? No. But if you decided to go that way I doubt the player would mind if you ended up telling him that his "orc traits" were really "Oni" traits. If you're just starting the campaign, you could even add some strange effects because of the things he doesn't know about his character.
While it is certainly up to you how fiendish heredity works, it generally works like this. Fiends like devils, demons, and oni make half-fiends, which in turn make tiefling grandkids. From there, they can become humans with sorcerer bloodlines or Racial Heritage, or the tiefling gene can popup again randomly. Now, since you are the GM, you can definitely make the ruling here that his father was an oni. Just a little food for thought.
Another option would be to have the father be the 'host' of the Oni, which possessed him after your PC was born. Just switching an Ogre for an Orc in that case would not be too much of a stretch.
The only problem with that solution is that it lacks the effectiveness of the reveal. He is looking for his father, but finds he is already gone and replaced by a fiend. Unless you make the orc father into a sympathetic figure (which would be rather unusual considering, and I doubt your half-orc's backstory leaves room for a loving interracial romance), then it just an anticlimax. He is looking for a father vs. son battle to the death, and instead he just gets some random fiend.
there are actually different kinds of oni that are formed when oni spirits fuse with different kinds of humanoids; the Ogre Mage is the most common, but there are more kinds in the bestiary 3 and in the Jade Regent adventure path. There's no existing type based on Orcs (because Orcs don't have much territory overlap with Oni, probably), but you could look at the Kuwa (Human-based) and Ja Noi (Hobgoblin-based) for examples of stats or traits an Orc oni might have.
there are actually different kinds of oni that are formed when oni spirits fuse with different kinds of humanoids; the Ogre Mage is the most common, but there are more kinds in the bestiary 3 and in the Jade Regent adventure path. There's no existing type based on Orcs (because Orcs don't have much territory overlap with Oni, probably), but you could look at the Kuwa (Human-based) and Ja Noi (Hobgoblin-based) for examples of stats or traits an Orc oni might have.
While that certainly may be true, I question the problems that might bring balance wise, since those are CR 4 and 5 respectively compared to the Ogre Mage's 8. Plus, Ogre Mages have useful things like a fly speed and at will invisiblity and darkness, all of which can define an encounter at lower levels. Of course, this is somewhat custom creature, so balance could still be preserved, but it still seems troublesome to alter the originally written creature that much.
But I am unsure if we are actually facing a problem here, since the complete replacement might not be necessary. Ogre Mages have the ability to change shape into any humanoid from small to large. So even if he starts off as a medium Orc (handwaved under the idea that they fill a somewhat similar niche, so they could produce similar oni), he could still take on an ogrish form. The only real problem I could imagine from the strictest RAW sense is that it would not be able to look like an 'ogre mage', and instead just an 'ogre', which can be misleading. Ignoring that small detail by slapping the typical fiendish red skin and horns for the final showdown/reveal while just saying 'magic lol' would simplify things.