Stuff to check because it can cause oscillations with stock settings: First of all, determine the fastest update rate that your ESC's support. Second, make sure they are set to use it (output page). Third, if you change something from the first two things, you should probably recalibrate your ESC's.
About tuning roll and pitch at the same time with EasyTune or OPTune: If your quad is symmetrical or only slightly asymmetrical, you can get away with it and it will fly much better than your current oscillation problem. If you really want to split hairs after tuning them together, you can tune just one at a time.