"Evidently" and "apparently" are used interchangeably. I would use this when I thought one thing was true, but I find out that something else is the case. For example: "I thought I could get tickets at the door, but apparently (or evidently) I was supposed to buy them in advance." "Obviously" describes something that is easily known. For example: "I didn't have my keys with me, so I obviously couldn't unlock the door."