Why does my car judder on hard acceleration and not when driving normally?

SOURCE: 2001 Audi A4 Avant 1.9 TDI

hey
well Fuel pressure will cause this concern as with a failing fuel pump, also a misfiring engine from worn plugs or defective coils will cause any bucking/jerking if u have as you try to accelerate, but this would cause a check engine lamp. A bad Mass Air Flow sensor can also cause a poor acceleration and usually does not turn on the check engine lamp.

SOURCE: Audi a4 fault

My guess is throttle body, it happened to me.  Try cleaning it beacuse its 700 installed.

SOURCE: 2005 Audi 1.8 a4 check engine light on and car now spudders??

FYI also when you get those codes you can look them up and get their description at http://www.check-engine-light.com

SOURCE: car runs rough when warm an accelerator is applied normal

P0306 is a misfire on cylinder number 6. The fact that you have oil on those plugs may or may not be causing it. The oil on the plugs is because of a leaking "internal" valve cover gasket. First thing I'd do is change the valve cover gaskets. Audi will murder you if you want them to do it (I've heard of people quoted $700 or more for this job). It's VERY easy to do. You can order the gaskets from www.ecstuning.com or www.purems.com for about $25 per side. I'd change them for sure, as they're a known issue on these cars.

Now, if your new plugs and changing the gaskets (and cleaning up of course) doesn't fix the misfire, you need to swap coil packs around and see where the code goes. The coil packs are the three parallel items on the top front center of the engine under the beauty cover. Trace the #6 wire back to see which coil pack it goes to. Then swap that pack with another pack, clear the codes, and fire up the car. See if the check engine light comes back and if so, scan the car to see what codes come up. If you still get P0306, then the failure didn't move, and the coil pack is not the issue (in your case, it's likely to be the wire, since you have new plugs and swapping coils didn't work). If the misfire moved to a different cylinder (one which is now hooked up to the coil pack that was originally firing the #6 cylinder) then that coil pack is bad and must be replaced (another known issue on the A4).

SOURCE: Audi a4 avant 2004. Which components need to be

Not necessary to replace any components, but the engine Exhaust Gas Recirculation (EGR) system needs to be cleaned inside together with the intake manifold, (both EGR throttled valve and intake manifold).