I don't think codeine inhibits metabolism of oxycodone or vice versa, I am yet to try this combo but have heard it is enjoyable from several sources. If you are taking codeine tablets with doxylamine I imagine they contain panadol/acetaminophen/APA or ibuprofen. You do not want to take more than a few of these as panadol and ibuprofen are harmful to your organs.
If you have much of an opiate tolerance then I doubt the likely small dose of codeine will add much in the way of effects but probably will add some. I don't find oxy particularly sedating where codeine is quite sedating, so it will probably make your buzz more sedating. I also imagine you would experience more itching and nausea.
Doxylamine succinate is probably my antihistamine of choice to use with opiates. It has a mildly sedating effect whilst reducing the itching and nausea that opiates cause. If you take too high a dose it is possible to experience delerient effects. I reccomend 25-50mg of doxylamine for opiate potentiation/antihistamine purposes.
Even in small doses the addition of codeine and doxy has the possibility to increase the effects from your usual dose of oxy quite nicely.