Can I varnish previously oiled wood?

Well I'm sure not a carpenter but here's what I would do, scrub the door down with "dawn" ( do U have that lq. dish washing soap there? ) it cuts grease really good, and would take the oil off, then if worried about mold and weather, paint it with marine paint ( the kind they use on boats) I did that to my cheap wood lawn furniture about 30 years ago and never did bring any of it in and it looks like new. Just pick a color you can live with for a long time as Marine paint is not cheap, or varnish = )good luck.