Add the olive oil to the Instant Pot and heat on saute mode until hot. Sprinkle the chicken thighs with salt and pepper.
Put the chicken thighs in the hot Instant Pot, in a single layer (work in batches if needed). Brown the chicken for 3 to 4 minutes per side and then remove it to a clean plate.
Add the onion and mushrooms to the Instant Pot. Saute until they start to soften, 2 to 3 minutes. Add the garlic to the pot and cook, stirring, for 30 seconds. Press Cancel to turn off the Instant Pot.
Add the dried oregano, garlic powder, paprika, ¼ teaspoon salt and chicken broth to the pot. Stir, scraping up any bits that are stuck to the bottom of the pot or your Instant Pot. (If you don't scrape it well, bits stuck to the bottom of the pot can trigger a burn warning.)
Stir in the orzo. Place the chicken thighs on top of everything else and close the Instant Pot lid. Turn the steam release valve to the sealing position.
Set the cook time to 4 minutes at high pressure. The Instant Pot will take about 10 minutes to reach pressure and then the cook time will start counting down. When the cook time ends, quick release the pressure by carefully turning the steam release valve to the venting position using the handle of a long spoon.
Once all of the steam has escaped and the pin drops down, open the Instant Pot lid. Check that the chicken has cooked through to at least 165° F using an instant read thermometer. Serve, sprinkled with fresh parsley and Parmesan cheese, if desired.