The reason to add oregano oil to another oil for OP is typically for infection in the mouth. Even below the gum lines like for roots, root canals, etc. But beyond infections, I can't think of another reason to use Oil of Oregano.
As for how much, I usually use as much as I can stand - since it does burn the mouth. For me that's usually 4-6 drops of the OO (Olive-Oil) I use. But that will vary.
One other thing to keep in mind is that many oregano oil capsules are mixed with olive oil. And the olive oil will probably be rancid. Not a problem for swallowing, but maybe not the most desirable to swish around in your mouth.