Add the cream cheese, cheddar cheese, and Monterey Jack cheese, garlic powder, oregano, salt, and pepper to a bowl. Stir to combine. Add 1 tablespoon of water a time until the mixture is smooth enough to be a spreadable paste.
Fill each jalapeño half with 1 tablespoon of the cheese mixture.
Place a filled jalapeño on a wonton wrapper, fold over the side edges, then using the tip of your finger, wet the remaining edges of the wonton with water and continue to roll. Repeat with remaining jalapeños.
In a large pot, heat oil to 350˚F (180˚F).
Fry the egg rolls in small batches until golden brown and crispy.
Transfer the egg rolls to a paper towel-lined plate.