The DIS is part of the ignition system, a gray flat module that sits on the passenger side of the intake; can't miss it. Some things known to go wrong: the connectors break, taken off and not reattached with enough heatsink grease, loose/incorrect mounting bolts , or the module may actually be faulty.
The "rear" plugs are more effort to reach, but with some patience + a long extension socket, doable without removing the intake. A mirror will help with inspection once you pull the wires off. Take your time to do it.
Since you believe you have oil in the plug wells, I would first make sure the wells were cleaned out and dry before removing the plugs. Don't want anything falling into the combustion chamber. If the plugs are stubborn, a very small amount of penetrating oil let sit for some time (overnight) should help.