Strange thing about Oregano is that is one plant that does not have any known antagonstic relationship with other plants. It is beneficial to most plants as it provides general pest suppression. It also increases humidity if allowed to spread amongst crops.
It is a short plant that can planted among and even under most plants and will enhance the humidity of the garden area when planted like this. Interplanting can help gardeners in a drought situation as inter planted Oregano will act as a living mulch while exhaling moisture onto surrounding fauna.
It deters Squash Bugs, Cucumber Beetles, which makes it a good companion for curcubits .. cucumbers, squash, pumpkins. It is also repulsive to the cabbage worm . cabbage butterfly which makes it a good candidate to plant near cabbage, cauliflower, broccoli and kale.
They fare well when planted with or in close proximity to most fruits, but grapes in particular seem to benefit from their presence as they repel many of the pests which prey on grapes. I have intercropped Oregano and Garlic at the base of Grapes and fruit trees and it worked out well.