Add the mayonnaise, cream cheese, and feta to a blender or mixing bowl and blend until thoroughly combined and smooth. Small lumps may be present, but large ones should be completely broken down. Stir in the oregano and onion mix until combined, then adjust seasoning with salt and pepper as needed.
Add the tomato, cucumber, and red onion to a medium bowl and toss with the olive oil and salt and pepper to taste. Dump the vegetables on top of the dip and serve with pita chips. Enjoy!